I definitely think buying one already built would probably be the cheapest route to go. I'm out of gun shows to look for one though.If you're petite I think a good pistol brace should work well, I say don't worry about a tax stamp and traditional buttstock anytime soon. Most likely the one you shot had a brace on, most 10.5 AR's are pistols not SBR's. Could ask the person you shot with to make sure if that's possible.
Do you like the look of painted guns? Possible that you could save quite a bit of money by buying a standard good quality black rifle and painting and switching out parts as you please, instead of building from scratch. But if you're dead set on building from scratch go for it.
I haven't ruled anything out. The gun I saw at the Kokomo gun show was just painted.
I'm looking for ideas and product sources.