I am upgrading my vintage Peugeot and thinking that this would be a good time to deal with my gearing. Right now I have 42/52 chainrings and 13-23T rear cogs. I’m old and kind of a wuss so even though these gears may work around here in Houston, I will be in trouble if I go somewhere with real hills.
Would some of you nice folks recommend what you think may be better gearing for me? Will a Shimano 12-28T 7 speed cassette be a direct replacement for my 13-23T cassettes?
Thanks again for your help!

Do you have freewheels or cassettes? Changeable rings or permanent? Need more info.

I think it’s a cassette, it’s labeled Hyperglide and the lock ring follows the cogs when I spin the wheel backwards. Thanks!

How many cogs are on that Hyperglide? 6? 7?

There are 7 cogs on my cassette.

It should be interchangeable with other Shimano 7-speed cassettes.

Thanks folks! I ordered the 7 speed 12-28T cassette.

You may have to get a longer chain as well .
The wear on the front rings may be an issue as well- check for "hooking " of the teeth.

Also, as you are going both smaller and larger in the range on the cassette you may incur shifting issues,
depending on the derailleur installed.

Many old school derailleurs, especially performance oriented versions, had a more limited
ability to wrap chain properly. Short cage vs long cage is a basic thing to check.

rusty

Need more info to fully help.
some images of the bikes drivetrain overall would help much.

when I read the term cassette on an old bike and cannot confirm the parts replacement path prior... “help “ may not be.

Try a smaller chainring too. For my steel frame Centurion Ironman I swapped from the original 52/42 chainrings to a few variations that depended on my fitness: 50/39 with 13-25 freewheel, then 50/38 with 13-28 (after I was recovering from injury and illness and needed a bit more granny gearing), and currently 52/39 with 13-28 freewheel, now that my fitness is improved.

That combo of a 38 or 39 chainring and 28 cog can make the difference between walking and riding when the legs are dead and lungs are on fire.

I went with Vuelta replacement chainrings. Good values, and I wasn't concerned about retaining original brands on my bike. The Vuelta SE Plus big rings are ramped and pinned, helpful with indexed front derailleur shifting but probably not essential for friction shifting. The smaller Vuelta chainrings are plain, no need for ramped and pinned small chainrings.

For 2018-'19 when I was recovering from injury and illness, I used mostly a 50T Vuelta SE Plus ramped and pinned chainring and 39T or 38T Vuelta plain ring (I swapped the latter around to suit my preferences for gear steps depending on the freewheel). Now I'm using the original Suntour plain 52T ring, and Vuelta plain 39T ring with a SunRace 13-28 MFM30 chromed freewheel.

I'm not a strong climber, but I've improved a bit from dead last on every Strava segment to middle of the pack, pretty typical for my age range. Our terrain in the Fort Worth area is mostly rollers, lots of short steep mini-climbs, stair-stepped over miles. Technically these may be 1%-2% grades over 4-6 miles, but on the road it's actually lots of short climbs in the 5%-11% range. There's a temptation to sprint up every climb and coast or soft-pedal the downhills or flats -- that's what most group rides do, which drives me nuts because the group gets strung out, then collapses, like an accordion. But I make better time pedaling steadily, not over-extending myself on climbs and putting out the same effort on downhills and flats. Less exhausting over the long run.