You have a 17x17' room = square, which is the worst for bass management. I am in the same boat as you. I use a diagonal set-up, which works reasonably well for me. Non-conventional, but works.
Is this an empty room, or does it have furniture in it? My room is the guest bed room, and the mattress acts as a large bass absorber, book shelf with books as a diffuser behind listening position. I made additional absorption from discarded shipping pallet wood and Roxul 180 (towels work as well). Lots of YouTube videos on that.
If you cannot add sound controls to your room, consider near-field listening (taking the room out of the equation), though your Klipsch are unlikely to be suitable for that. Digital Room Correction is NOT going to solve the node problems in a square room, sorry.
Re TT, lots of option in the ~1K range. Depends a bit of what features you want (automatic vs manual, belt vs. direct drive, color options, integrated phono preamp or not). Re cartridge, MM for sure, maybe something like an Ortofon 2Mblue or bronze. With many ~1K TTs a cart is supplied with it. Possibly start there, and if you want upgrade thereafter.
For amp, I would look at second hand market. I would not worry too much about brand (stick to majors, IMHO), rather whether you like the look, whether it has phono stage built in (see above re TT options).
Good luck!