Well, let me be the first up to bat here…
Most turntables made, both new and vintage, play 33rpm (most 12"s) and 45rpm (most 7"s). Some older models will also play 78rpm, but it doesn’t sound like you’ll be listening to too many Bing Crosby shellac records, so that’s moot.
Be careful of flea market turntables. Cartridges tend to be junked, and drive belts tend to be stretched beyond repair. Ebay might be a better bet.
My advice depends on how much you want to spend. If you only want to spend $20 or so, flea markets are pretty much your only bet. Be aware, however, that aside from the problems you mention above, some replacement parts for some older tables (i.e. Bang and Olufson) are impossible to find. As well, a flea market turntable is likely to do actual damage to your precious vinyl, especially if the TT has a ceramic cartridge.
If you are willing to go up to about $100, you can find a reasonable selection of 20-year-old Pioneers, Sansuis, Hitachis, and the occasional Marantz on Ebay. These were build pretty solidly, and are common enough that you can get replacement parts easily. Be aware, however, that you are going to want a new cartridge anyway. A Grado Black cartridge will run you $40–it’s pretty much the best in that range.
If you are willing to spend $250-300, you have a few other options. A new Music Hall (www.musichallaudio.com) or used Rega 2 will fit the bill, and sound a hell of a lot better than anything mentioned above. Sounds like this might be a little more than you want to spend, though.
One last thing–you might need a phono preamp if your receiver or amp doesn’t already have a phono input. Radio Shack’s the cheapest game in town–their $30 battery powered unit is amazing for the money.
Oh, and links:
www.needledoctor.com
www.elusivedisc.com
www.ebay.com
www.amusicdirect.com
But if you do decide to go the flea market route, get a Garrard or Dual if you find one. (I definitely wouldn’t go playing an ultra-rare first print Misfits single on one of those, though.)
Hope this helped.