Kinda hard to lurch into the world of acoustic room treatment until you have an idea of what the room sounds like and what you want to change about it.
For just getting started, try a computer, a decent sound card or USB interface, a decent (meaning pro audio) set of speakers, a good set of headphones, a couple of mics and cables, and a good piece of recording software.
For software I would go with Reaper, without question.
Mics and cables - start with basic performance mics - a Shure SM57 and an SM58. They're affordable, good quality and dead useful. $ 100 each.
Interface? Start with a basic USB 2 channel interface like
a Mackie Onyx Blackjack. The onyx preamps are very nice for the price. $ 150.
Headphones? The sky is the limit here. Look for a closed back pair in the $50 range to begin with.
Speaker / monitors? Again, you're looking from a hundred bucks to thousands. But stay away from stereo speakers here and maybe spend a bit more. I have a pair of Event TR5 powered monitors that are quite workable. If you can afford to get monitors with 8" woofers, just do it.
For a computer, look for one step below a hot gamers computer and then back off all the fancy graphics add ons. Look for a muscular hard drive, a CD burner and perhaps double video monitor capability.
That's it for a basic rig. All your effects are in the software, so you need nothing outside the box. Learn the basics of Reaper and spend your time making music instead of getting hung up on techie stuff. Sooner or later you will start hearing stuff you want to change and that is when you can begin to get fussy about the room. Your ears will take you where they want you to go.