You won't be sorry, Howard. On cleaning air guns, DO NOT USE FIREARM CLEANING EQUIPEMENT ON AIRGUNS!!! Just wanted to make sure you heard me :-). All you need is a few patches and some Goo Gone or Simple Green. Note that both of those are cleaner/degreasers, not solvents. Most, if not all, of the firearms solvents will damage airgun seals. I use an Otis flexible cleaning kit, works fine in the CFX. Lots of guys just use weed wacker line, with a ball melted on one end to hold the patch. Also, NO METAL BRUSHES!!! Truth is, airguns need cleaning very seldom, maybe once every 3-5000 pellets. And expect accuracy to drop off immediately after cleaning for the next 100 or so shots. What leading happens in an airgun actually helps improve the sealing and accuracy of the gun, so the less cleaing, the better.
You mentioned Beeman Silver Tips, I know they have several pellets that start with Silver, but none that end with Tips. Silver Jets, Silver Arrows, Silver Bears, seems like I'm missing one. Silver Arrows are pointed, and too heavy for the CFX, even in .22. Also not very accurate in my experience. Silver Jets can be good, Silver Bears can be very good, depending on the rifle. So far, I've just been breaking mine in with Superdomes, sub 1 inch groups at 30 yards even with the stock trigger. Also, unless you open it up, you won't have much use for any lubricants. Maybe a drop of that Pellgunoil on the cocking linkabe, and that's about it. Do NOT get any kind of petroleum based anything around the breech and chamber, serious bad mojo if you do. Makes things go bang, which is not something you want with and airgun.
Regarding hold, the CFX is probably the most forgiving springer out there, as long as you don't use a death grip, it'll probably do what you want it to. Just get comfortable, and try to do everything the same way all the time. The rifle will do the rest. Have fun.
Dave