I have a bicycle with Presta valves.
Should I buy a Presta pump or a Schader pump and a Presta-to-Schader adapter?
You don't actually have to decide :-)
For bicycles you want a pump that is capable of pretty high pressures (at least relative to a car) and most bicycle pumps can do either Presta or Schrader valves. Many floor pumps have a reversible head (two heads in one). For frame pumps it is common for the pump head to be convertible between Presta and Schrader.
Unless you have a reason to support Schrader valves life will probably be simpler if you have your pump set up for Presta valves, but I think it is a good idea to also carry a Presta-to-Schrader adapter with you. They are very light. If the rest of your world is Schrader then it might be more convenient to just put adapters on both of your wheels and pretend that they have Schrader valves. Moving the adapter around on a regular basis will probably get old.
Why not both? Any good track pump will support both valve types. Do get one with a gauge though.
Your on-bike minipump will probably support both types as well, though gauges are rare.
On the off-chance you want to use a car pump, having one of these in your first aid or tool kit is a good idea, or leave it on the wheel permanently as a cap.