Sounds like all you need is a decent drill/driver. I strongly recommend getting something that is part of a system. I have a bunch of Ryobi stuff, which is from Home Depot, but there are several other brands. Typically they have a battery (e.g., 18V) that is compatible with a whole bunch of different tools. Usually there will be a starter pack of drill/driver + battery + charger, but sometimes with multiple tools at a good price, and then you add additional tools (hammer drill, circular saw, etc.) as you need them, sharing the battery(ies) and charger.
- Drywall - Actually, you don't want to use a drill at all for drywall. Just use a Drywall Saw:
Hanging TVs, picture frames, etc. - Use a drill/driver to drill pilot holes through the drywall into studs and then screw through the drywall into the studs.
Assemble Furniture - Can be done with a manual screwdriver, but a drill/driver will make some of it go a little faster.
For screwdriving only, almost anything will do. But 12V or more is best, and given current pricing I would recommend an 18V system for more power when drilling as well as the ability to add other tools later.