And the MP-5 is probably your best bet in that application... Ballistol is more of cleaner and protectant for barrels and wiping it down to prevent rust!!!
Any good gun oil should work. For pivots I prefer an oil around 20-30 weight, light enough for good penetration, but heavy enough for good lubricity. I also prefer synthetics because of their stability over time, nothing to evaporate or get gummy. Often I will apply moly in a light weight carrier, wait for the carrier to evaporate, then oil. I have had good luck with the Birchwood Casey synthetic gun oil.
I use synthetic motor oil very sparingly on the joints. I have an oiled cloth I keep in a plastic bag for my rifles. I wipe down every rifle after I shoot it, especially the barrel.
The new liquid Moly by Guntec looks good. It looks like a flowable moly. With heavy loading on joints, you want a bit more than a thin oil, but often thick Moly, which is great for heavy loading, does not get into the tiny gaps to get where you need it….enter a flowable moly!
I use a motorcycle chain lube, containing moly, on the cocking pin. It's typically thin enough to flow into the joint and then thickens and is tacky enough to stay put. I happen to have a can of PJ1 Black Label...but there are quite a few varieties of motorcycle chain lube with moly in them.