Is it not possible to replace the chain rings? Just replace them both with smaller ones?

Possible, but there are limits sometimes at to how small you can go and as to what is readily available.
Easiest is the rear cassette, probably the least expensive as well as long as your rear derailleur can handle it.

As mentioned above, 38T is as small as you can go on your crank, and isn't worth the bother unless your 39T is worn out. I'm with Chas and John E that swapping to a smaller big ring will make it more usable, though. I run a 48T or 50T big ring on my road bikes with 13-X cassettes. (Well, a 52T on one of my lesser-used ones, but that's with a 14-24T freewheel for about the same top gear.)

Yep, the cassette swap will be the easiest way to get the job done; easy is good.

Even easier: if you have a good bike shop nearby, you should take your rig by there and tell them "I want you to sell me an 8-speed cassette with the biggest cog that will work with this derailleur. It'll be a little more expensive than snagging one on the big auction site, but you know the size they give you will work, because they'll be able to test the shifting right there at the shop. Since it's literally a 5-minute job to swap a cassette, they'll probably do it without charging you for anything but the parts.

I like caveman's idea unless you have a cassette lock ring tool, chainwhip and chainbreaker.

I would suggest a 12-32 over 11-32. Nearly uniform spacing in gear ratios. I believe that necessitates a Sunrace cassette rather than Shimano or SRAM, but it'll work fine.

Lastly, I would also go lower on the front large chainring. At least down to a 48. My experience (with one bike) indicates that a smaller gap in tooth count up front helps the RD exceed max tooth count in back. And it can go at least two teeth beyond max.

You likely have a 1056 RD with a 28t max cog, I have nearly the same (same vintage 600 RD with same max) and am running a 30t in the back. I would't be surprised if a 32t would also work. Only a test fit will tell. The thing about starting with a 12-32 and possibly going down to a 12-30 or 11-30 is that your chain only needs to be shortened a bit more to fit.

Good luck!

Definitely go to Ebay or your LBS before you trot over to Rivendell where they would probably charge the snot out of you for just a simple cassette.

I with you. I now have learned I can only change the larger Chainring. Mark at Rivendell suggested I do as you and others have suggested. He suggested I go with a 11-28T or a 11-32T with a 46 or 48 T chainring. They stock the 11-28 and 11-32 for $30. They didn't have the chainring but he found one for me on a closeout and Excel sports for $39.95.

Now my only decision is deciding between the options. 46 or 48T and how large on the rear cassette? I'm playing around on Bikecalc.com trying to understand and learn.

I understand what you are saying but they have cassettes for $30 and Mark actually went on line and found me a 130 mm Sugino 48T front chain ring. Check out above response. I went with 2 bike shops just doing little quizzing and they wanted to replace crankset, cassette, RD, chain, etc. That's why I came here to try and get honest opinions. Ayou ll of have different opinions but they are narrowing down to where I feel good about my direction.

Another thing, I had not ridden my bike in 15 years until I read one of Grant Peterson's books. I have now made my bike comfortable and a joy to ride. All i need is a little lower gearing and I'm good to go. I feel somewhat grateful and "obligated" to Rivendell as if it weren't for Grant's philosophy I would have left my bike in the garage attic and never ridden it. Does that make sense? I may be old school but if I can spend a little money with them I feel is it "my" way of paying them back for getting me back in the saddle at 58 years of age. My knees are already getting better!

I'd go for a 13-26 and a triple on an 8 speed bike that sees hills.

If you can keep your shifters, it won't be much more money than replacing your chainrings. A new FD or BB is cheap if you need either. Anything else is just a half measure.

32/42/52 or 30/40/50 for a quick road bike.

24/32/46 or 28/38/48 for maximum comfiness

There's no need to give up close gaps on your cassette. You lose a lot of magic when you put a 11-28 or a 11-32 on a 7 or 8 speed road bike. 11 or 12t sounds pointless for you anyway.

You can get all flavours of 8 speed shimano cassette from wiggle for less than $20. Chain reaction cycles, merlin cycles or amazon are other good places to buy parts/ tools for cheap.

Sugino makes great triples. You have a much bigger range or triples to choose from with an 8 speed bike than with an 10 or 11 speed bike.

You could get a suitable Sugino triple from Riv (or not pay the tithing and get it for less on amazon).

It sounds like they are taking care of you well. Most of us would love to have a shop in the neighborhood that does that, instead of trying to sell us whatever the TDF or Ironman riders are using.

I hear you.

Support the guy that supported you. They went above and beyond for you, so I would repay them by giving him my business.

God luck!

Where we are its very hilly a couple of ours have 11- 34 teeth 8 speed on rear, other than the chain length, one would have to buy a longer arm RD.

On one of my bikes I've a 20 on the front (triple) & 36 on the rear, its the only way on steep inclines to keep the pulse rate within limits !!

I would personally get a modern Shimano Deore LX long cage RD, a wide range cassette (11-34?), a longer chain and ride away!

I obviously don't stress keeping my bikes period correct.

The gap between gears could be pretty large in cases, but unless you combine the above with a triple, you aren't going to get much lower gearing.

Compact (110 mm BCD) on the front with something like my favorite chainrings (48-34) would be good if you want to keep a tighter geared cassette.

There is a reason LBS's cost more, and you are reaping the benefit. If you currently find yourself using your top end gear on descents, get the 11-32 and match it with a 48t up front. 52x12 is nearly identical to 48x11. If you never ever use it, get the 46t chainring.

It it sounds like you'll soon be much happier - the world is a better place with a happy cyclist in the road. 39x32 gives you a very nice low road gear - especially if you are jumping back in after a 15 year of break from cycling. My 40x30 low gear on my gravel grinder is plenty low for very steep hills up to 11% grades.

Looking at what's actually available in an 8-speed version, you'll find 12-32 and 11-32t. The Sunrace 11-32t has a rather big jump from 15-18t that I wouldn't want myself.
Sram and Shimano offer 12-32t in 8-speed, with only a 18-21t jump where the 3-tooth progression starts.
Since the 48t ring won't eliminate the need for a longer chain, I would consider that merely an option, and likely to cost at least $30.
I recommend buying the X-grade KMC chain, far better than their Z-series chain for just a few dollars more.

Lots of good gearing advice here but there's a few things you might consider.

Rims and tires.

If its just your standard everyday rider and not about speed, yet you want to climb, consider a performance lighter weight rim plus a lighter tire. Drop that rotating mass!

If you want speed plus making life easier during ascent, same as above but maybe something more aero (plus type of lacing). Its another entire realm- rider weight, not too aero where its a handfull in crosswinds, etc.. For tires, spend for a higher quality, faster and having lower rolling resistant.

I don't know all the hype stuff, nor do I follow it but my modern ride with a mediocre lightweight rims / lacing is a slug with cheap tires. A tire swap to something quality totally transforms the bike. Nothing to do with gearing.

For a few of my older bikes, I like to explore tire types. My heavier weight '57 JC Higgins Clubman scoots pretty good thanks to some light ally, single wall, non-hook bead clincher Weinmann rims. The tires are vintage Michelin 28" wire bead but have a small raised center. Placebo effect, I don't know but it rolls nice and light, the bike 'feels' respectable fast... all things considered. Even at 15 lbs more than my lightweight rides, I have no issues taking it to the hills!

Now for the discussion of hills and comparing to riding in the open prairie's with endless miles of constant cross or head winds-

Even a constant 10 mph headwind is going to bust you sooner or later. The game to beating the open winds is rim / wheels and tire choice.
The open flat lands gets old too and why I cherish the climbs. And while riding the open windy flats, my bike geek thoughts are of having a Zipper fairing.

And, while we're perhaps aspiring to progress in various racerly advantages, my "secret weapon" to beating the low-gearing game s to develop a rider position on the bike that compliments a more frequent lifting off of the saddle to let my legs stretch out.
Getting the saddle forward often goes against rider's intuition, but makes for a more-effortless lift-off, and I can thus forego lower gearing in lieu of a more aggressive standing stance that not only counter-balances higher pedaling torque but also lets the entire body "take up the slack" in my pedaling motion, such that my knees see a more-limited range of motion and thus are less apt to become sore or even injured when pushing the taller gears.

After developing this more-forward fit on the bike, I then concentrate on developing the coordination that allows me to avoid any critical level of stress from arising in my palms, wrists, elbows, shoulders or abdominals.
Riding the sharp rollers here daily does wonders for my ability to handle steep pitches, and has relatively little to do with gearing or of absolute levels of fitness. Coordination and good form go a long way, which is assured by the daily practice.

It seems that for the riders who moved here and promptly donated or sold their bikes, the ever-present hills were a curse, and probably why so many of my bikes were found at thrift stores and garage sales. For me, they (the foothills) are more like my salvation, forcing the daily exercise of my habits, coordination and fitness.

So I still advocate for the larger cassette and "bigger" rear derailer, knowing that in the future that any needed swap to a "tighter" cassette is just a $30 and five-minute change-out.

Odd, I found just the opposite - Sunrace was the only one I could find in a 12-32 and only Shimano had 11-32.

Anyway, if it were me, I would be throwing on the 12-32 for exactly the above reasons and going with a 48t chainring in front. But no matter what you do, if you don't like it and decide to change, you weren't wrong, you just took a step down the path toward greater happiness.