If you want to keep two kegs on tap, I'd suggest owning three or four kegs but you can start with two.
You'll need a co2 tank (can be kept in the fridge if it's a 5# or 10#), a regulator, and some lines. You can use "picnic" taps, or you can buy some faucets and shanks and go through the door eventually. You'll need some lines, too.
To keep it simple at first (you can always add more stuff later- it's easy!), I'd suggest:
a co2 tank (5# is ok, but a 10# will last longer between fills, unless you have a leak!)
A regulator. A single gauge is fine, but some people like to have different pressures for different kegs. I'd go with the single for now.
A T fitting (or a WYE) for the kegs. I like the ones with valves so you can turn off the gas to one keg.
Make sure you have check valves installed, so you don't inadvertently ruin your regulator.
Then, to dispense, you need one black quick disconnect for each keg/line. You'll need one cobra tap (picnic tap) and 8-10' of beer line for each.
For the gas, you'll need one gray quick disconnect for each line/keg and the line from the "T" or "WYE" at the regulator. The gas line just has to be long enough to reach the kegs, but I like mine a little longer so I can pull the kegs out still connected to the gas. I think they are about 5'.
I think that's about it!