Inexpensive starter system

I am looking at setting up a turntable system. I have speakers and somewhere between $400 and $600 to get form my records to my speakers. I would prefer to get a nicer turntable and a lower end amplifier to stay within my budget.
Used, of course...

Dual 1019 turntable $50-100
Entry level Grado, Stanton or Audio-Technica cartridge $50-75
Hafler or Dynaco preamp $50-150
Hafler or Apt Holman amp $100-150

The good thing is that you will have plenty of room for upgrades. ;)

Still, you will get enough information to actually enjoy the music sort of in a way the artists intended.
if you could stretch to say $750 you could get very, very nice starter system. a brand new rega r1 w/ cart would be ~$395 and a used rega brio integrated (which has a mm phono stage) would be $350ish. that amp only offers 40wpc so speaker match is somewhat impt. arcam also makes some nice integrateds with phono stages that can be had used in teh $300-$500 range (there is actually an alpha 3 listed now for $200 that you may want to check out - that plus the new rega r1/cart would be right at your $600 number). a one box amp saves on hidden costs since you only buy one ic cable (table to integrated) and there is only one power cord to upgrade down the road.
What Wrtickle said. Can't go wrong and it will sound better than 90% of what is out there.
I think it would help if we knew something about what speakers you have, what do you know about setting up a 'table, what kind of music do you intend on listening to, what is your listening room like, etc.
Agreed, basic rega will serve you very well...sometimes that's better than cobbling odds/ends together.
For beginners, I don't recommend used equipment. I think it's better to get something with a warranty, and has a much lower risk of loose connections, cracked circuit boards, and leaky capacitors near the end of their lifespan.

Plus, the new gear brings so much transparency, speed, clarity, and high signal-to-noise that the older gear seldom has, and at very good prices.

Get an integrated amp from Cambridge or NAD for under $350.

For a turntable, skip the MDF plinths, the rubber band drive, and cheesey construction for a solidly built, easy to set up and use Audio Technica PL-120 direct-drive turntable with precision aluminum castings, weighing in at around 25 lbs.

You can get it at Amazon for about $205, or for $299 from LPGear with decent AT95 cartridge, better mat, and protractor. If you go with Amazon, spend $99 and get the Ortofon 2M Red, which is a great match for this turntable.

For reviews of the PL-120, check out this review at Crutchfield and download Issue 11 of ToneAudio magazine, which has a pretty favorable review from a longtime high end belt drive aficionado.

There is a link to The Absolute Sound's review of the 2M Red and Black here, and if you Google "ortofon 2M red review" you'll find plenty more.

Also, the NAD and Cambridge integrated amps I mentioned here don't have a phono preamp, but the Audio Technica turntable has one built-in. And if you upgrade later, you can always turn off the internal phono stage and get a nice outboard one from Cambridge, Parasound, NAD, Bellari, etc.