[Regular Joe]

I used cleaning rods for decades with no apparent ill effect, but the potential is always there. These days, I use a kind of patchworm of my own making. It's just a piece of masons' line with a loop at one end. I put the patch thru the loop, then run the loose end thru the bore. I put the loose end back thru the loop as well, so I can just keep pulling it thru for multiple passes, changing the patch and what ever it gets wet with, or dry patches to end with.
With a .22 it will almost never have lead deposits. When you're comparing ammo, it can be good to start with a clean bore, then fire 5 or 10 rounds to "season the bore" with the lube of the bullet variety you mean to check. Then fire your accuracy rounds. When you're done with one ammo type, clean the bore with 2 passes of swabs soaked in Hoppes', then 2 dry patches, and repeat the seasoning with the next ammo type.
It is a good idea to keep a nice brass cleaning rod on hand, in case a bullet ever gets lodged in your bore. There's really no other way to get it back out.
In testing ammo, do try some of the Federal Lightening from walmart. It's cheap, and popular as a fairly accurate load. The big trick in finding your preferred ammo is to compromise between accuracy and price. With a bit of testing, you can probably find a plinking round for around 4 cents each that is accurate enough to keep the fun in the game.
BTW- While you're out looking at things, don't forget to get a pair or 2 (they're cheap) of shooting glasses, and some kind of ear protection. I'm already deaf in higher frequencies, so I usually forego the ears, but I get stuff hitting my glasses all the time.