Newbie questions RE: Technics SL-3200

Hello everyone!
I am the new owner of a Technics SL-3200 turntable that was given to me by a friend who is moving. Along with the player came a large collection of records, mostly Jazz.
While I know this player is not terribly high-end, I'd like to make the most of it in concert with my modest sound system. I'm would like some sound advice from you more experienced folks on how best to procede on a tight budget.
My only decent pieces of audio equipment are a Rotel RA-971 amp and a pair of speakers that were built for me by a friend using GR Research 5.5" drivers and Scanspeak tweeters. They sound nice to my ear, anyway.
1) I will need a phono preamp to make use of my turntable. Which units would you recommend for someone on a modest budget? (sub $100 used, if possible)
2) Will a new sub-$50 cartridge make a noticeable improvement in sound quality on this turntable? If so, what cartridges would you recommend for classical and jazz?
3) Finally, since I know nothing about record players, how should I adjust the anti-skate and arm weight? Is there some objective way to find the "right" settings without special tools?
Thanks a bunch for your help!
Mika, nice table, welcome to a new world of analog enjoyment. There are several excellent phono preamps in, or around your price range. I like the Rotel, there is a Parasound for sale today, though I have never heard one, and the Creek and Musical Fidelity ones are quite nice too, though they may strech your budget. If your budget is absolutely and totally fixed, and you can only spend $150.00 or so on both preamp and cartridge, I would recommend the Radio Shack phono preamp that costs around $35.00 and a better cartridge in the $100.00 range. That would be a Grado Red, Shure M97ed, Ortofon OM20 or Audio Technica AT440ml, in order of warmest to most detailed. My personal preference would be the Shure or Ortofon. If you are set on allocating your funds as described, the Grado Black, at around $40.00 is the logical choice. A new cartridge is an absolute necessity to preserve your budding record collection as a used cartridge may have a ragged stylus and damage the groove walls.

There are many free tweeks that you can try. A light, but solid stand is one. Removing the rubber ring that fits between arm and headshell is another. You can put a dab of rope caulk on the headshell or arm where it rings.

As far as setup goes. Start by folowing the manufacturers recommendations on tracking force and set anti-skating to match. You can tweek this by ear, but do not stray too far. A protractor will be necessary to determine where the cartridge will sit in the headshell. There is a free one to be downloaded from the net. Perhaps a kind member can direct you, as I forget the site. One can be bought for $20.00 or so, if need be.

Best of luck.