First, you should be sure that the crankset is actually worn -- cranksets last a long time, and some teeth will look like they are worn (but they aren't) due to aiding shifting.
The bearings aren't in the crankset itself -- they're in the bottom bracket, which is pressed/threaded into the frame. In your case, your bike has a Hollowtech II bottom bracket, and you can use Hollowtech II compatible cranksets (or change the bottom bracket type, and use some other crankset).
When choosing the crankset, you do have to have bottom bracket compatibility, crank lengths, and if the crank clears everything on your frame when installed -- for example, most mountain bikes will have interference if you stick a 50 tooth crankset on them because the geometry of the bike is not setup to take this.
I'd suggest just going to a local bike shop to make sure you do need a new crankset, and chances are they'll have some Hollowtech II crankset that will fit your bike anyway, if needed.
Another reading of your post suggests that the splines on the bottom bracket (thing the crankset goes onto; contains the spindle which the crank arms rotate about) may be worn (is this what you mean by shaft?). In this case, you'll need a new bottom bracket and crankset. I'd leave this work to a shop if you don't want to buy the tools (bottom bracket tool, big wrench, crank puller, etc.).