Keeping it simple, but still wash your hands
I’ve often found it difficult to clean my firearms while wearing gloves, this gets right back to the problem that I have often come across when handing the AR15 rifle with them on. There are smaller parts to take apart on the M4 Carbine and even though I have to get my hands dirty, I can’t get to all of the parts with gloves on. There have been times I only fired less than 20rds through a rifle and I wasn’t in the mood for a full firearm disassemble. If I have a firearm that has gone on a camping trip like my Marlin 336 lever action or a Winchester Model 70 bolt action, I still clean them after every trip even if they have not been fired. Moisture can get to these types of firearms and I have had many wars with rust in the past.
There are traditional cleaning kits that may work for you, but since I have bent rods cleaning firearms, I strongly recommend against anything but a once piece rifle cleaning rod to prevent damage or issues. Boresnakes will speed up the process of cleaning your bore and avoid the problems of putting cleaning patches, but you still need to use lube and wash them on occasion. Otis gun cleaning kits can fit in a rifle stock, your pistol grip or your butt stock depending on how many tools you think you want to store there.