Not 58 or 60 cm if you are 5' 8" tall. If you have a short torso, you'd be on a 54cm with a longer stem. If you have a long torso, you'd be on a 56cm with an appropriate stem.

My wife and daughter are both 5'8", with the wife having the long legs and the daughter having the longer torso. Their proper fit is as described above.

Try some road bikes at your local bike shop. Explain to them what you'd like to do - how you'll carry your commuting gear, whether you'll ride at night, how to mount fenders, etc. They'll steer you to what they have that can meet your needs.

Many folks like cyclocross bikes because of the braze-on mounts, wider tire clearance, cantilever brakes (room for fenders), but road feel. I've not ridden one, myself, though.

A touring bike will have wider ranged gearing, and will be very strong. The geometry will be more oriented to stability when loaded. Typically, gear shifters are on the bar ends. I have a tourer and it is very, very comfortable to ride. It's not nimble, though.

PG