The problem with buying new is that it is too damned expensive if your ear is educated to better sound. I am currently using a VPI Prime Signature 21 with a VPI Shyla cartridge. An Audio Research PH-7 phono preamp. I just tried out an Audionet PAM 2 preamp (15 years old) and I was literally floored. I couldn't stop listening to records. I will reeplace the PH-7 with something that has the clarity, depth, warmth, and fluidity of the Audionet. I hope! Because I cannot afford $10,000 plus new for something of the Audionet's bliss.
The problem buying used is that if you buy online you can't hear it first. So, you have to do research. For example, when I upgraded from an ARC PH-3 to the PH-7, I knew I liked ARC phono preamps, so I researched their entire line. I've owned ARC Reference preamps, so I know their sound. Perhpas you might feel the same way about BAT.
I decided the ARC PH-7 was what I could afford and would give me the best sound for my $. I couldn't find one for sale in the United States. I called every Audio Research dealer listed on their dealer list. Then I began calling Canada and I found one. And I have loved it much over many years. But having heard the Audionet, I know the clarity and detail I am missing.
There are many brands that are known for solid "honest" turntables. VPI is one, but a whole bunch of people are going to jump in here now and tell you other solid brands.
If I had $15K, I'd probably spend about $8K on a new turntable and arm. Around $1500 on a decent cartridge. Maybe $500 on cables. Then the other $5,000 on a good used phono preamp. I am more inclined to buy electronics used than turntables. But that's just me. I once bought a used VPI TNT 3 and kept it for years, but VPI makes very solid turntables.
Again, I'd research the brands that are always well reviewed and begin looking at those brands and perhaps deciding on a model. Most dealers don't carry a very big stock of analogue equipment, so you might end up buying everything online, and you information will have to come from reviews.
It sounds like a fun adventure. Good luck!