Another way to go that I've also wanted to build is a direct drive turntable.
A custom plinth could be built for a Technics SP10, SP15, SP25, or one of the Denon drop ins. That would just require a tonearm/cartridge and you're in business.
Don't forget that a build like mine also requires a motor/housing & speed controller.
All told with phono stage and cartridge included, I've got about $2000.00 invested in parts and materials.
I think a good direct drive table as mentioned above can be built for about $900.00 in parts and materials, depending on the table chosen.
I'd also be very happy to help you along the way with any information or ideas I can give you.