As above, buy a ONE-PIECE stainless steel or carbon fiber cleaning rod for home.
For the range, the Otis is the best of the pull-throughs, but remember, ALL pull-through cleaners WILL break sooner or later, even the Otis. This can leave you with a plugged bore and an extraction problem.
If you insist on using a bore snake, don't keep washing and re-using it too long.
That weakens the material and they WILL break off in the bore, leaving you with a real problem on how to get it out.
Also, every time you pull a snake through, you're pulling all that grit and fouling right back through.
To keep dirty solvent and debris out of the receivers, buy a bore guide. These are plastic tubes that lock into the chamber and receiver and act as a cleaning rod guide as well as keeping crud out of the action.
For other equipment:
Either carbon scraping tools to clean carbon from the bolt and bolt carrier, or a chemical carbon remover like Slip 2000 Carbon Killer.
Buy a couple of GI type M16 toothbrushes.
A nice accessory is a plastic solvent application bulb. This is a plastic bulb with a long tip that allows putting solvent on the brush or patch or into a solvent port on the bore guide. This prevents dipping th ebrush or patch in the solvent bottle and contaminating it.
Buy these bulbs from lab supply houses or from Brownell's listed with Accu-Bore bore solvent.