They have Rega so I was thinking of starting with a p1.The P1 doesn't really bring much to the party. Everything is noticeably compromised and it doesn't upgrade gracefully. The P2 isn't much better, but the Rega P3-24 (which is just inside your budget) starts strong and offers ways to upgrade as your ears demand over time--outboard power supply, upgrade the platter, upgrade the tonearm. Another alternative: If you shop online and google for the best deal you can score a Technics SL1200 mkII for about $350, or the M5G version (better tonearm wire) for under $500.
If you go with a P3-24 you'll definitely hear a different presentation than digital. The P3-24 has good 3-D imaging right out of the box and a relaxed presentation that eludes most CD players until you get into the stratospheric price range. Even then, you're still making do with a 16-bit dynamic range (64K increments of amplitude).
To keep it under $1K NEW, I'd go with a Technics SL1210 M5G, Foculpods to replace the feet ($25), a Herbie's mat ($72) and record damper ($22), and Ortofon 2M Blue ($199) or Audio Technica AT150MLX ($299) cartridge.
OR
The Rega P3-24 with Ortofon 2M Red ($99) or Blue ($199) cartridge to stay just within budget or a tiny bit over. The 2Ms are a good match with the P3-24.