Multimode fiber has a bigger core and uses less precise optics than singlemode fiber. This makes the transceivers (SFPs in your case) cheaper than their singlemode counterparts. This also means they can't shoot over as long of a distance as singlemode can because the light gets scattered within the fiber and has poor long-range characteristics.
OM3 is a manufacturing specification for multimode fiber. This should probably work well for your needs. Wikipedia has a good comparison of different multimode fiber specifications:
You'll need compatible (matching) SFPs on both ends of the fiber and they'll need to match the type of fiber (singlemode vs multimode). Since the limiting factor for speed in this case would be the SFPs, you'd be fine to get OM3 cable installed and regular gigabit SFPs. When you're ready to upgrade to a 10Gbps connection, you would need to upgrade your SFPs and possibly your switches.
You'll also need to take into consideration what sort of environment your fiber will be in. If it's run inside a building, you'll be fine with regular fiber, but if it's run through the ground or in an area where it's susceptible to damage, you'd be better off with OSP (OutSide the Premises) fiber cable with sheathing.