Before you start, be sure to have a good set of tools. The slotted screws for the barreel band and attaching the stock to the action are pretty generous, the slots are wide and deep. a regular screw driver will work, no need for a gunsmithing set yet. The bolts holding the barrel to the receiver are hexhead. Have a good set of Allen-type wrenches. The size is pretty standard but once you get to souping up your 10/22, the other sizes will come in handy, all the way down to 0.050" for some of the accessories like re-zeroable target turrets of scopes.
As others have said, the 10/22T is a step up from the base models, but still well short of what you can make the gun out to be. IMO, you should also try your hand in modifying the original parts to see what you can do yourself and it'll give you a better understanding of how the gun works and what mods will help or not. You'll replace the parts anyway.