My most recent Rega (I've owned two) was the current P3 which I upgraded like crazy. This was documented at the old place, but all of that info is lost.
I had more tied up in it after the upgrades than the MoFi Ultradeck that I currently own. The MoFi is easily superior.
Rega tables are funny. While I didn't love it for numerous reasons, I still think they are good values for those of us that live in the U.K. By the time the U.S. importer gets their cut, not so much. And I'm not sold on their "lighter is better" philosophy. I won't buy another.
The Pioneer PLX-1000 is a good choice. Budget an extra $200 for upgrades to bring it to the next level- headshell and tonearm damper. Add a suitable cartridge (Grado or A/T) and you are still under budget.
@mcherry owns one with the upgrades and really likes it.
The MoFi Studiodeck is an even better choice but adding a cartridge puts you over budget.
No matter what you end up with, you'll want a digital stylus forge gauge- less than $15 on Amazon.
Whether one of these choices or a restored Dual or Thorens- any are light years better than an LP60. You'll be a happy camper.