For most people and most situations a light-ish mountain bike/hybrid with medium-width road tires is a good bet. I also recommend not caring about shock absorbers aside from making sure they aren't rusted out if you want a bike that has them.

I usually recommend that people find a build-it-yourself shop that uses donated parts, they will either teach you how to do it right there and then you get a bike or they'll sell you a Frankenstein bike that suits your needs, is relatively cheap, and supports this culture of sharing and reuse.