Welcome! We love spending other people's money.
And it's never been a better time to get into audio (low priced/high value gear is abundant and cheap digital source material is available).
First know what kinds of listening you prefer: genre(s); sonic attributes you most often focus on (bass, highs, detail, imaging, timbre, male voice, female voice, other instruments)
Second tell us: budget; full room description; current system; what media you're interested in (vinyl, CD, hi-res); schedule to complete
Third learn: music appreciation (many of us barely know what we're listening to); room acoustics (Floyd Toole's "Sound Reproduction" would be an excellent start); various audio technologies that apply to you (are you more of a hobbiest, are you interested in tubes, want to do kits, does vinyl interest you)?
Fourth research gear: internet (lots of fluff and crud to go through); stores (limit how much you listen to each day with your favorites and take notes); shows (good to find out what's out there, veto stuff, and talk to manufacturers); local clubs (get a feel for different in-home solutions); in your home auditions (the only true way to know if it'll work for you)
Fifth purchase: finally enjoy!
IMO it all starts with your available room (unless of course you do headphones). Most audiophiles over spend on gear for their given rooms (that, and budget, are what headphones are for at home). Room size/shape will dictate what kind of speakers will work best. Treatments are only bandaids and can't fully cure bad (small/ill shaped) rooms. Room isolation dictates the background noise level, how loud and when you can play. Shared or dedicated can dictate setup.
Next I'd start with speaker selection as they have the toughest job in the sound reproduction chain (to change one form of energy to another, electrical to mechanical). And speakers are a personal matter (presentation varies by imaging, level of detail, amount of bass output, etc, etc, etc). Obviously especially true if you go with active speakers (highly recommended) which can start at less than $300 for a good pair (plus stands). And I'd finish with source(s) as they interact the least with the other components.
