I need to replace my kickstand because it broke, so I need tips like is there any strategy on how to choose and install that part? Do they all fit into that hole where they need to be attached, or are there different sizes of stand for different bikes?
Pletscher and Greenfield both make decent kickstands. The most common kickstand is a single leg model that attaches just behind the bottom bracket. Pletscher also makes a double leg kickstand that mounts in the same place and Greenfield makes a kickstand they call the Stabilizer that attaches near the rear dropout on the non-drive side.
The double leg kickstand is nice if you need the bike to be stable while you load cargo or if you use a single-wheel trailer like the B.o.B Yak or Ibex. On the other hand it is a, small, bit more trouble to use since you have to lift the bike a bit to all the legs to fold down.
Most kickstands seem to come in a size that is too long. The leg(s) need to be cut to a length that is appropriate for your bike. It's easy as long as you have a hacksaw – on the Pletscher you just measure from the ground to the center of the bottom bracket and then find that dimension on the where it is marked on the kickstand and cut it off.
Depending on where you park the bike you might want to get a foot for the kickstand either to protect a floor or to provide some resistance to sinking into soft surfaces.