A few things that will help:
A cleaning jag. I recommend the TC Jag which makes the aligned unnecessary in my opinion.
Cleaning patches. No need for a kit.
A range rod. If you shoot much, you will want one. You can make your own or pick something up on eBay. Save the rod in your gun for hunting as they are generally made to be light and not to be used all that much.
I guess this all would be in a cleaning kit but the components I mentioned will cover it.