Anything is possible, and something is better than nothing… maybe… or better wait until you can spend more. Really carefully chosen $1k will get some sound out of them… pleasing? I need help on that. But splitting $600 for integrated electronics and $400 (Rega?) for table would sound OK. Just for reference if I was looking for matching components I would think of a budget of about $20,000 for electronics… you could do so,etching fairly complimentary for $10K. The good news is they are pretty efficient speakers (91db) so they don’t need lots of power.
Someone will have to chime in with specific recommendations in these price ranges. The closest thing I have experience with is a $2K integrated amp (no phono stage).