If you're just looking to get started, run what you have (or fill in the gaps) before buying all new. For 3-gun specifically, come out to a match and watch how things are done. It's going to be very difficult to determine what you need/want unless you have a little experience. It's way too easy to spend a lot of money & then find out you don't like your shiny new gear the first match you go to.
A lot will depend on your personal preferences, so I'll list what I would be going after were I to be starting over with what I know now. This is for 3-gun specifically, though the pistol category would also apply to USPSA. The would would also change significantly depending on your chosen division, the recommendations below would be for Tactical Optics, by far the most popular division at our local matches. Also you'll eventually want a lot of additional gear beyond the guns, so make sure you account for that as well. Don't burn all your money on the guns and then be reloading from your pockets.
Pistol
High end: 2011 in 9mm (too many options to name, just do your research)
Lower end: Striker fired 9mm (M&P, Glock 34/17, etc.) of your preference
Shotgun:
High End: Benelli M2
Lower end: Stoeger M3000
Rifle:
High End: purpose-built AR for competition w/ 1-6 variable scope (custom, or there are numerous companies offering off-the-shelf 3-gun ready rifles in lots of price ranges)
Lower end: any reliable AR w/ a red dot or irons
As long as you're a confident reloader and sure the gun will run well with both loads, I'd say go for it. From a beginner's standpoint, I'd say that's pretty intimidating. JMO. You could also buy a .40 Glock or M&P & run a 9mm conversion barrel for 3-gun.To each his own but I don't agree with the 2011 in 9mm. Why not a .40 with 155 grn pew pew loads? I think it is a much more versatile gun as changing ammo will get you right back in USPSA lim or lim 10 Major PF.