People's reasons for doing vinyl are different. If you want it to beat your CD player for $300 all in, that may be tough (though not impossible). With a $50 thriftshop table, a $150 cart, a few dollars in vibrapods or spikes (depending on what else is under your table) and a good protractor, you can get good sound (assuming your phono stage is up to snuff). But I would not know if it would 'beat' your CD player. People's tastes are different.
Rhljazz' point about sticking to the silver discs is one which has credence, but for a different reason. I think the MONETARY COST is actually a limited input if you buy used. Far more important is the cost of time and effort. It takes time to find a TT, to learn to set it up, to look for vinyl, to clean the records when dirty, and then, if you end up not appreciating it, it takes time to get rid of the stuff.
For me, the lower monetary cost was one reason I went to vinyl. I can find any number of old records in fine condition which are 25cts to a few dollars. If I wanted to buy those on silver discs, it would cost me several dollars per disc used and $10-20/disc new. In order to listen to 1000 classical albums from the past over the next few years - albums I had never heard before - it would cost me $5,000-15,000 in silver discs + no dollars for my CDP... or... it would cost me $1,000-3,000 in vinyl, a few hundred dollars for a record cleaning machine, and then something for a vinyl setup. At the end of it, I could resell the vinyl and the setup or I could sell the extra 1000 compact discs. The CDs cost me more upfront, and the CDs will lose more on my investment than I will lose selling the records and vinyl back out. To me, for that reason, vinyl is the low cost solution.
If you want to keep your experiment well below $300, I'd suggest the garage sale or thrift store TT route. Phasecorrect has mentioned the families of tables I would look for. There are a bunch of them out there and they punch above their weight (cost, not lbs).
