Certainly what you plan to use it for is a major consideration, but personally I look for versatile pieces. The other thing is availability of parts, accessories, etc.
For a first time rimfire plinker you cannot go wrong with a good old semi-auto, rotary clip fed Ruger 10/22. If you get one, get a stainless model. These are much more durable and the finish will always stay nice. When you look at the used ones at the shows, look for the best NIB or excellent condition one you can find. Stay away from ones that show any amount of wear. Expect to pay $125-$175 for a blued standard, to $175 to $270 for a stainless model. Of course you could always buy a new one, but better to bargain hunt.
Another excellent choice is the Remington 552 in either ADL or BDL (plain or fancy finish). These babies are very versatile since they accept LR, longs, and shorts. They are semi-automatic, tube fed, and hold as many as 17 rounds (shorts). They are very accurate and less than $200 used. You'll see at least one at nearly every show.