If you don't want to spend a ton of money trying this out, the best bang for your buck is a vintage direct drive unit. Direct drive is driven directly by a motor with no belt, are extremely precise, and will serve you well with no maintenance basically forever. There were a ton made in the '80s, and they can be had for a song. I picked up a Technics SL-1600 for like 40 bucks. It is a work of art compared to what most companies are putting out these days. The Audio Technica series zowie mentioned is a fine intro if you don't feel like looking around for a used table - they're basically a poor man's Technics SL-1200, and one of them has a preamp built right in if you don't have a receiver and want to run it directly to a separate preamp.
There is some work involved in setting up a table - you need to align the cartridge, set the tracking force, anti-skate, tonearm height (if possible), make sure it's grounded properly and a handful of other chores. It can definitely be worth it though. Or you can try to find one locally that's already set up.
A little addendum to my previous post - depending on your tastes, it may not ever be worth it for sound quality alone. But it sure is fun, and a it can be an interesting intro to the science behind audio technology if you read the science lit.