Count me as someone who spreads a build out over several months. It gives me the chance to hunt for deals and save my coins for the next parts. I save money on everything by buying some items used, taking advantage of industry discounts (I work in the outdoor industry so have access to some), and shopping sales when all else fails. I also don't keep extra parts around very often, and when I do, they tend to be much older parts that I usually don't want to put on a new build). I pay MSRP for very little when I build a bike. Consequently, I'm pretty sure I actually do end up saving money (though because I spread everything out over so much time, I lose track of detailed expenses).
But, that's not a process that a rider new to bikes (and especially one new to working on bikes) is going to be successful with. A big thing to keep track of is compatibility. I've lost count of the number of times here on mtbr, people are trying to match up parts that don't work together because they shopped on price first and thought they were getting a great deal without verifying compatibility.
I also tend to want my bikes built the opposite of the way manufacturers like to do it. I want my non-wear parts to be better quality. So frame, suspension, wheels, and brakes. And for wear parts, I'm usually willing to sacrifice some bling. Modern drivetrains are shaking that up a bit in that higher end chains and cassettes often are less expensive to own when averaged out over their lifespan because they last so long, even though they're very expensive on initial purchase.
You actually don't need that much when it comes to tools, unless you do this sort of thing often enough to make bearing presses, frame prep tools, etc worth the purchase. Having a shop do these tasks is much cheaper. There's a break-even point, though, so if you do enough of these jobs, the tools become worthwhile. I will probably never own facing tools for frame prep, though. They're very expensive, the cutting ends have a limited life (and tend to be expensive to replace), and it's so cheap to have a shop do this that it just isn't worthwhile for the home wrench.