If you are not comfortable removing the side plate then by all means don't do it. Many a gun has been buggered up but someone who was unsure of what they were doing. Some of that foaming gun cleaner that some folks use should work well for you though I have never used it a lot of the guys swear by it. Just hose it down inside the action and wipe it off.
As for the ammo, just stay away from the wally world bulk packs and don't just buy the cheapest stuff you can find. Stick with standard velocity pure lead bullets. You have a high quality firearm use quality ammunition. I buy my .22 ammunition from Champion Shooters Supply, but I'm just lucky to have one of the counrtys finest Anschutz and small bore target dealers close to me, and can go in and buy just one box of everything, then go back and buy bricks of what works.
Champion Shooters Supply LLC