The stock scope rail should work fine if you want to save a few bucks. My first 10/22 has the stock rail on it and it has worked OK. That 10/22 is the one I do new stuff to to try out before modifying my other 10/22s. It's got a cheapo Tasco 3-7X25 on it with .22 rings. The other modified 10/22s, however, have Leupold bases, rings, and scopes on them (except for the one in a plastic 2/3 scale MG42 stock). A fixed scope between 4X and 10X should do any job you have specified. For variables, I would go 3X-(up to)10X or a 4X-14X. I prefer the Leupold mount (or other similar mounts) as it centers the scope with the receiver. For the dove tail rails, most rings have one side fixed with the other side doing all of the clamping. Because of this, the scope, although parallel with the bore, is usually off center. Not too big of a deal but not preferable to me.
With all of the mods you have planned for your rifle, don't discount on spending a little more for a good scope. Leupold Vari-X IIs are going for a pretty good price nowadays as they are being phased out. Unfortunately, they usually go for $200+ new. They are gauranteed though.
Although the Tasco has worked OK also (for 12+ years), it cannot compare with the Leupolds for image quality. Don't let those incredible deals on BECs and BSAs persuade you. They are as cheap as they are priced. I did buy a BEC and a BSA to see for myself. Spend your money elsewhere. They'll do in a pinch but build quality and optical image are well below average.
Recently bought a Burris Black Diamond to be on top of an AR but cannot comment on its actual use as the AR it's destine for is not here yet. It seems to be well above average from just holding it in my hands and looking through it.
You probably can't go wrong with Pentax, Nikon, Burris, Weaver, Simmons, or even higher end Tascos and Bushnells BUt I don't have any experience with these other thant he low end Tasco. The Euro scopes are probably out unless you can find one used.
