The list of what you can do with a 10/22 is ENDLESS. Yes you can truly have it anyway you want, all it takes is a little imagination and $$$.
Above are a few of the Custom 10/22's I have put together for myself and friends.
For a heavy barrel target type gun I really like the Nordic Components AR-22 Receiver Chassis.
This is all aluminum and then you add the AR-15 Buttstock, Pistol Grip and Free Float Tube of your choice. As per Barrels it has been my experience that there is no noticable difference in accuracy or velocity between the 18" & 20" Bull Barrels. Now my buddy will argue that with me telling me the 18" are more accurate.
As for Triggers I feel that that is another key ingredient to accuracy (well at least for me). I have done my own trigger jobs. Used Volquartsen and or Power Custom Target Hammers. Had TT Shooter out in California do trigger jobs for me. And lastly used the new KIDD Drop in Trigger Kits designed for the new Aluminum Trigger Housings that new 10/22's are shipped with. To me the best results are either the TT Shooter rework or the KIDD Drop in Trigger Kits (which are both about the same $$$).