While I dont want to be a thread crapper or turn this into a good/bad mfg one, my personal experience with RCA TV's since the late 80's through the 90's has been very poor.
I believe that Thompson Consumer Electronics makes all GE and RCA tv's (since GE bought RCA/NBC a decade or more ago). As such, if you google the SCI.Electronics area you'll find that numerous RCA sets primarily fail due to really horrible tuner components and then a whole list of secondary failures. I seem to recall also something about very bad rates of tube failure, similar to Zenith due to some batch of cheap tubes (for a few years) from Mexico or South America.
Sadly, at the thrift stores, old late 70's/early 80's RCA sets are often in better working condition than the later models. The problems I typically see in old ones are of course horrendously burned in screens, fuzzyness or overall red colors (tube failure not component failure). The ones on the newer ones are collapsed vertical deflection, channel tuner doesn't work, pincushion/geometric problems, or simple no-power on..all component failure.
Actually I often see brand new 24" tv sets for around $129 or so.. They probably don't last long either, but may work.
Persoanly I would not pay more than $30 for a 25" TV thats 6 years old.. Also be sure to look CLOSELY at the tube and look for burn-in.
In the old day burn in was easy to spot: a light grey tube looked brown. Now with dark tint it's harder, but with the TV off look at the RGB stripes on the tube. If you see dots in the middle of them all of the tube, it has been on a lot and burned in. The tube will be less likely to give a good color picture and closer to its' death.
Some tubes shadow masks make each trio of stripes a "cell" by itself leading you to believe there are dots, but the clue is to look for smaller dots filling each cell on each color stripe.
Very light dots are usually okay. Large ones and you wont like the picture and it will burn out all the faster.
No one bids on TV's on ebay because it's too costly to ship them.