The best quote I ever read on the topic of brewing to save money went something like this:
"Home brewing to save money on beer is like buying a boat to save money on fish."
If you sole goal is to save money, then you can do it, but you won't have great beer. Just buy canned extract kits on sale, boil it on your stove, and bottle-carb. You'll have dirt-cheap beer with less than $100 investment in equipment.
For a little more investment ($500-ish?) you can move to a BIAB setup and do small-batch brewing or partial-mash full boils.
Or you can spend $2,000 on a complete all-grain setup with kegging. You'll make great beer, but you won't live long enough to recoup what you spent in beer savings (unless you drink a lot more beer). In this case, you'd do it because it's a fun, rewarding hobby, rather than to save money.