Paul -- I've got 10 years on the single battery that came with my 18V Dewalt cordless drill. It's getting tired though, doesn't hold a charge as long . . I may just stop by Home Depot today.
As for the tools, buy a quality multi-tool and look what it can do -- there's a clue in the answer to that question.
First, a small set of high quality screwdrivers and a good drill would be at the top of my home tool kit list. Followed shortly by pliers (needle-nose, Diagonal Cutting Pliers, Wire Strippers, Tongue and Groove Plier) as required. If you plan on doing plumbing you can start adding Crescent/adjustable and pipe wrenches plus a number of plumbing specific tools. A quality crosscut handsaw should also be on the list as well as a good Pry Bar.
Hammer -- sometimes, but around the house I use a drill with screwdrivers much more often. That said, I've got three different weight framing hammers, two finishing hammers an old ball peen hammer and a rubber mallet; they don't see much use.
My old Porter Cable 6 1/2" circular saw hasn't been off the shelf since I rebuilt the bedroom closets. Great saw, just nothing for it to do here. That said, a
Dewalt 6-1/2 in. 18 Volt Cordless could replace it; it takes the same battery as the drill.
Go
HERE and start making a list, it adds up quickly.