Yes, it needs to be cleaned after you use it. I use a Midway vibrating case tumbler because I have one for other reloading. But you don't need to go to that expense for your purposes. Here's what I would do if I didn't have the tumbler.
1. Take a small plastic bottle of soapy water with you to the range. (I use a 20 oz. plastic Coke bottle, but something smaller will do, maybe a pill bottle.)
2. When you take the fired cartridge case out of the gun drop it into the bottle of soapy water.
3. Whenever you get around to it - a day or two, or a week later - shake the bottle real well, dump the cases into a larger container and flush them with clean water.
4. Punch out the spent primer.
5. Wipe out the inside of the case and primer pocket with a cotton swab, or for a real good cleaning wrap a little steel wool around the swab.
6. Wipe the outside with one of those green dish washing scrubbies or some steel wool.
7. Make sure they're dry, and re-prime.
8. Shoot 'em up and do it all again.
You can reuse them until the new primer will no longer stay in the pocket - probably forever since there's no real pressure to stretch the brass as there is when firing a bullet from the cartridge case.