Forget the rod and guide. Buy some string trimmer line, not large diameter. Tie a pull loop for a few fingers in the end of 3-4ft of the line, and about 1/2"=3/4" loop in other end.
I have always used Hoppe's. If it's not the best, it's certainly good enough.
Insert .22lr cleaning patch in loop and feed it through the open chamber out through the muzzle. Pull patch wet with bore solvent through the bore. Allow to sit in bore for at least 15 minutes (Let the solvent do the work). Run several dry patches through to bore to remove residue and dry the bore. You can repeat this, but a perfectly clean bore is not needed.
The lube on 22LR also acts somewhat as a bore preservative, and leaving some in the bore is a benefit. You can patch out remaining residue before firing. Don't overdo it.
PS, I have never been able to keep a cleaning rod permanently straight, except for carbon fiber rods (overly expensive). Bent rods amplify bore cleaning wear.
I clean all my rifles in a manner very similar to what Greg mentions, but I use VGF pellets soaked in bore cleaner. Brownells sells them here. Instead of tying a loop, I use a hot piece of metal to melt a sort of plug onto the end of the trimmer line and that acts as a stop for the pellet. Just feed a pellet down your section of line, then feed the line into the chamber end of your rifle and pull it through to the muzzle. Easy.
I clean all my rifles in a manner very similar to what Greg mentions, but I use VGF pellets soaked in bore cleaner. Brownells sells them here. Instead of tying a loop, I use a hot piece of metal to melt a sort of plug onto the end of the trimmer line and that acts as a stop for the pellet. Just feed a pellet down your section of line, then feed the line into the chamber end of your rifle and pull it through to the muzzle. Easy.