You likely want a floor (track) pump - something that looks like this:
(Image from here)
Most good floor (track) pumps have support for both Presta and Schrader valves, usually through two opposite ends of the chuck:
(Image from here)
If your pump only supports Schrader valves but you have a Presta valve, you can go to your bike shop and buy an adapter for Presta->Schrader for around a dollar, each. (The reverse case is rare to occur, but adapters do exist but they're around 8 dollars a piece)
To pump up a Presta valve, you unscrew the nut, tap the nut to let a bit of air out (so that the valve isn't stuck), push the chuck onto the valve and lock it, then pump, tighten the nut. Dust cap is optional. Schrader is identical to the procedure on a car.
As for which pump to buy, make sure its rated to an appropriate maximum pressure, has a good warranty and has good reviews. Going with a good brand helps too, but you don't need to spend much. I've been using a Topeak Joe Blow Sport II which I got for around 30 bucks with no problems for the past 2 years.
Frame pumps are a different matter, but they're primarily for people going on longer rides who won't have access to a floor pump in an emergency. Shock pumps are for people who have air suspension to fill their forks, and are also a different matter.
A non-exhaustive list of quality manufacturers include: