What type of drill should I get?
A basic drill/driver will meet the needs you mentioned.
What is drill/driver?
I think a cordless one would be more convenient. I own the Dewalt 20volt max but you could get away with 12volt max if you are not going to be doing heavy drilling. Dewalt's and their batteries are not cheap, I have set of craftsman cordless tools in another location and they are more affordable. There are many options, Rigid is another.
You want one that has a clutch or adjustment stops so when you are assembling cabinets you can set it to a weaker torque setting to avoid driving the screws too deep.