Everybody makes a CLP these days. You cannot go wrong with what the manufacturer recommends, since when they do testing, ostensibly that's what they use. The fact that they suggest that you use Clenzoil with their guns may be because they really think it's great, or because they get something in the bargain from Clenzoil to say it.
I have never heard of the stuff, but I'm sure it works just fine.
I put my first M-16 together back in 1978, and this guy comes into the shop the other day and insists that I use Aeroshell grease to put his AR-15 upper together. I say "uh, why?", and he tells me "Because it's Mil-Spec - it's what the military uses". I tell him that this is all well and good, but I don't have any Aeroshell aviation grease (you know, since it's used for aviation...) He goes on to tell me that "the military" uses Aeroshell and he wants me to use it on his gun (I don't know why, I guess he wishes he was in "the military" or something?), so he brought me some. "How nice" I say and put it in a bag to use sometime next week when I get around to the 5-minute job of assembling his "Mil-Spec" AR-15 upper. He agreed to pay me $50.00 to assemble this tack-driving beast of 1/2 of a pea-shooter, so I guess I shouldn't complain.
But I digress.
At about $8.00 per quart, Mobil 1 5W30 (automotive oil) is a great gun oil and a quart should last a lifetime.
For cleaning, I use a myriad of different products depending on what I'm cleaning and what I want to dissolve (Copper, Lead, Carbon, Powder Residue, etc.)
For protecting - I use several other products - depending on what type of gun I'm protecting as well.
Some guns like a little grease and a very tiny bit of oil. Some guns like only oil. Some guns run better with a PTFE (Teflon) lubricant.
What I can tell you is this - a little bit of oil is good, but a lot of oil is usually not better. Most people put way too much oil on their guns.