CLP is perfectly capable of acting for all your uses as the name claims. Some diehards would rather use separate clearer and oils, but it's mostly a Ford and Chevy thing for the average shooter. Real, real diehards are addicted to Hoppes and can't imagine using anything that doesn't smell and isn't toxic.

A step up from BreakFree CLP, and more expensive, is Gunzilla or Rand CLP.

If you live somewhere that is humid and you don't use the guns for longer periods of time between cleanings, then a true gun oil might be more appropriate. It's been decades since I lived anywhere humid, so no recent experience in that regard.

The Tuf-Cloth is fine for wiping guns down, that's what it was originally developed for. The cloths do dry out over time, so just make sure it is actually laying down a protective coating.

For serious cleaning, I use M-Pro7. Non-toxic and no smell and does the job.