I will give you a VERY specific recommendation for your question about a drill: Lowes has the Bosch DDBB180-02 on sale right now for $99. It's an 18v cordless drill/driver that comes with 2 batteries (they'll be either 1.3mAh or 1.5mAh). The retail price on two battery packs is $99.
I own the next model up (same batteries, though - 1.3mAh for mine) and built a 6x8 chicken coop with plenty of 3" screws in 3-4 charges and was never waiting on a battery to charge while I was working. It comes in a box that helps you keep the drill, charger, batteries, and a couple bits tucked away and together. Runtime tests performed by PM and other publications/blogs consistently show Bosch, Milwaukee, and Makita at the top of the cordless tool game with DeWalt occasionally taking a top 3 spot. That said, if you end up not doing much, a cheaper model and/or corded drill may be all you need. If you plan on using it more than a couple times a year or for a heavier-duty project, IMO go for this one.
In regards to building up a set of tools, it completely depends on what you are doing - tool collections seem to grow over time as you take on more projects. You could visit Harbor Freight with $50 and come out with a lot of hand tools that should work well for you as a new home owner: 1"x25' tape measure, torpedo level, claw hammer, SAE & Metric combination wrench sets, screwdriver sets, nut driver set, & an aluminum speed square. Go to Lowes/HD to get a variety of bits for your drill/driver - lots of #2 philips screwdriver heads in various lengths as well as a set of drill bits and you will be looking for projects to tackle left & right.
*edit*
Thegoblinchief's advice about not buying stuff until you need it is a good way to not waste money! If you get on Pinterest or spend time dreaming up projects, your wishlist for tools is going to explode. Actually using what you imagine you'd use (or tackling projects you'd like to) is a different ballgame. There are a lot of tools you can buy used, but battery-powered tools are an area you'd want to stick with new. It's one of those categories like razors and printers where the consumable part is where the cost comes into play, so buying an older, used NiCad 14.4v drill with no working batteries is going to be a complete waste of money and a frustrating experience.