"1) will this end up costing me more money that if I just bought the darn thing."
That depends. If you consider your time free, then you might come out on the positive side if you use a reasonably-priced cabinet hardwood for the drawer fronts and a low-cost secondary wood for the drawer sides, bottoms and other internals.

But this assumes that you build an all-wood tool chest. If you include metal drawer slides and other hardware, it's extremely doubtful that you'll spend less than going to Sears and buying a good Craftsman metal tool chest (or to Home Depot and buy a Kobalt chest, or whatever).

If, however, you consider your time to have some value, you may be better off purchasing a very nice, $1200 ball-bearing slide metal chest and build other things instead. It's what I did.