How to choose the correct all purpose screw driver or drill
Most low voltage drills are targeted toward hobbiests than anyone else, and a 7.2V drill is likely not going to be much use for driving screws.  It will likely do fine for drilling holes, but there is generally a pretty strong relationship between voltage and torque. 

If this is something you'll be doing enough to justify the purchase, I'd look for something 14V and higher from a reputable manufacturer (Bosch, Dewalt, Makita, and Milwaukee spring to mind). Avoid the cheap store brands or cheap imports (I'm looking at you, Harbor Freight), and read some reviews from websites or magazines that are aimed at contractors (I usually start at FineHomebuilding - they do a ton of tool reviews).

Finally, keep in mind that the majority of what you are paying for are the battery packs.  This means that you can generally get better deals on tool combo sets than individual tools because they'll share batteries.

BTW, on your protruding screws you'll want to back them out about a quarter inch before setting them the rest of the way - it's easier if the driver isn't at full torque when you start.