So I'm going to replace my first rim........
 

I picked up a nice Schwinn Tempo this winter. The rear wheel had a significant wobble, but I thought I could true it up. After 30 minutes of adjusting with poor results) I took all the tension out and found a tacoed rim. After reading the forum its probably a goner. It has a variance of about 2-3 inches.

I'm not building a classic bike, so what is a good inexpensive rim to start/learn with? 700×36......replacing a Weinman 513-622..........

How about a Sun CR18 rim? They're reasonably priced.

Or, if you're bloodyminded and persistent, once you've got it de-laced, you can whump and thump that tacoed rim back into shape, more or less, but it'll never be perfect. I had great fun one night doing this to a badly warped Rigida Blue label. Hammers, 2x4's plywood shims of various thickness, a trash can, my knee; the kitchen sink. I learned a lot, and ended up with a usable rim. The funny thing is, it's only about 2-3mm out of true now, but I can't get it quite that round, which I thought was going to be the easy part. Admittedly, I have very limited experience in wheel building.

if using 23-28mm tire width, you can go with sun m13ii rims (and sapim db spokes).

i build mine right in the frame.

the rim erd is 610mm, and sheldon can tell you most everything here: Wheelbuilding

there used to he a very simple hub measurement page on his site, but it seems to have been replaced with a long mathematical treatise. darn.

Lascaux's experience doesn't match mine. I've never been able to refresh a badly bent rim, and when I did place enough tension on the spokes to get one to finally run straight, the end result was flat spotting / out-of-round. So the best approach here is dumping the back rim for a fresh one.

Schwinn's Tempo was a very nice bike, made from Columbus tubing. (Full disclosure - I had an '87 and the major problem I had with it was the easily-bent rims and the lack of clearance for fatter tires. ) It's worth sinking some coin into to make better.

If this were my bike I'd probably build up a replacement around a Shimano cassette hub, using DT Alpine IIIs for the drive side (which requires the dish and has to be more abuse-tolerant) and DT competition or Wheelsmith double-butted spokes for the non-drive. The rim would be a Velocity clincher with eyelets - or I'd swap both rims in favor of these - Velocity Escape Tubular Rim, 700c 32h, Black

Much as I like the CR-18 for utility builds, it's a bit chunky for the Tempo. The Sun M13II is a decent choice if you can still find them. Sun Alloy Rim 700c M13 II Black 32 Hole

You'll want to replace any bad spokes with fresh ones, and replace all of the nipples with fresh brass ones. The new spokes should at least try to match the lengths of the old ones.

If you get into trouble, you can consider taking the rim and the old wheel to a bike shop and having them perform/complete the transplant operation.

I agree, you can probably get your old rim into the useable range, and if it's a specific rim that's no longer made and hard to replace, it may be worth the effort. For a wall hanger, definitely; for a commuter, maybe not.
The tools needed are a stack of magazines, a flat floor, and a piece of wood that exactly matches the distance between the barrel of the hub and the rim. also recommended: patience, soothing music, beer, and some extra spoke nipples.

If you're not going to use the Tempo for loaded touring, Rivendell has a nice deal on Velocity Twin Hollow rims in the 36 hole version. Soft rims are the Tempo's only weak spot, even the 87's came with those terrible Rigida black ones.

Well I got lucky.....I had a vague recollection of picking up a wheel with a bunch of broken spokes. I dug it out and sure enough its the right size! It was totally unmarked, but exactly the same height at axle and overall, when compared to a known wheel.

I cleaned it up; zip tied it to the damaged wheel and swapped it over. So far, so good.... I'll try my hand at trueing tomorrow.