I use the Beall system on about 97% of all my turnings.
The three wheel set up works well for small items such as pens, handles, small bowls. Its not suited well for medium or larger bowls or even deep bowls. While you are working with one wheel you have limited space on either side to move your project.
The balls work okay on the inside of small bowls but to get enough speed to really make them useful you'll need to crank up the speed on the lathe. I have these and very rarely use them. If all you're doing is small bowls they would be fine, if you're doing other things such as spindle turnings and pens and the like you might be somewhat disappointed.
The three individual wheels with the adapter is what I use almost exclusively now. They work very well on spindle turnings from pens to large handles. They also work well on platters, the outside of any size bowl and the inside of most bowls. However if the bowl is small or very deep it may be a challenge. For small bowls where I can't use the 8" wheel I will usually hand buff or wet sand, but I normally don't do small deep bowls anyway.
Whichever system you go with you'll want to de-fuzz the wheels. Coarse sandpaper on a flat board works well. Wear a mask because the lint can be pretty thick. You'll want to place the sandpaper on the board then up against the wheel, it gets all the loose fibers out of the wheel. If I accidentally loaded too much compound on a wheel or need to clean up a wheel (once a year) I repeat the process.
The Tripoli does great at removing small scratches on raw wood. If you are buffing a finish be careful as the Tripoli can be aggressive and it is easy to go right through the finish. I don't use the Tripoli compound very often.
The white diamond is great and what I use on everything. Its less aggressive and does a great job at producing a beautiful shine/sheen, even on bare wood.
I do not use the wax whatsoever. If you use it use just a little bit. If you use too much you get smudges and that is nearly impossible to remove. The wax doesn't last very long and is a magnet for fingerprints as well. Instead, I use a microcrystoline wax, wipe it on lightly, wait a few minutes and then I buff with the wheel marked "wax", basically is a clean and bare wheel that buffs the microcrystoline wax to give a great shine that resists fingerprints.
I use danish oil on most of my turnings. No matter what finish you use make sure it is cured, not just dry to the touch. While the surface is dry it may not be fully cured and if you go through the dry layer into the uncured finish, well, you'll have a big mess. I always wait two weeks between the last application of danish oil before I buff. Maybe too long, but better than having to try to fix smudged oil and having to replace a buffing wheel. For resin items you probably don't have a finish on them and can go straight to buffing. I would suggest buffing with the white diamond then a microcrystoline wax. The tripoli will be too course and probably put scratches in the resin. One other option that I use a lot when turning say a resin pen is after I wet sand to 3000 or 5000, I use a plastic polish, rub it into the resin blank, then turn the lathe back on and buff it with a soft paper towel. Works amazingly well. Of course that is before the pen is assembled.
Hope some of this helps.
Damon
