+1 on more expensive to build than buy, I have built several bikes and the "scope creep" is a real thing. You will need several tools which most people don't have to do it correctly and things like hi-quality cables and housing are not cheap either and can escalate the cost.
It's a super fun and rewarding experience though so don't let me deter you! Like I said, I have done it but learned several hard lessons the hard way (chainline is a real thing, shifters and derailleurs are not universally compatible, I once used a GXP crank with a Shimano BB, etc. etc. etc.). I now ride a "complete" bike but I am in the process of swapping out the rather entry level components 1 by 1.
Your LBS should be able to get you into a hardtail with 90 percent of what you're looking for for $800 new. Then you'll know it's set up properly from the outset. You can swap out brakes and other bits as you go.
Once you have a nice stockpile of old parts, THAT'S the time to build your frankenbike! Which reminds me, I would really love to have another single speed. Dang now you got me thinking!