If you really are after a cheap TT to listen to a few LPs, IIRC one or two of the current Pro-Jects and Rega have an inbuilt phono stage but they are nothing special.
Also bear in mind, if this is simply an experiment and you are looking in thrift stores and the like for an old cheap TT, that all those $20 70s and 80s amps/receivers e.g. Pioneer/Sony/Marantz etc often have very good phono stages, most much better than current budget stages
. If you are lucky, you might also find an old Meridian 100 series pre/power with MM or MC card on eBay for little money.
Many of these old amps need little more than a good swab down and deoxit on the switches. Again, look carefully at the caps for leakage.
P