Let's see if I can answer the rest of your questions:
Q. Are you better off using a fast burning powder or slow burning powder?
A. Depends what you want, really. There are a lot of variables in play, besides what you want to accomplish.
Q. Is one easier on your barrel and brass?
Brass will "live" longer with loads that have less max pressure. This is because they will stretch less each fire -> resize cycle. As far as I know, the killer for barrels is bullet velocity and burn temperature. The more overbore a cartridge is (roughly the more powder volume per caliber diameter), the faster the barrel will wear out at the throat area. Likewise, a faster bullet velocity will wear the barrel faster. This is "throat erosion." This is why a .30-30 barrel will last basically forever, but a 7mm Rem Mag will lose its accuracy "edge" after a couple thousand rounds. I know these comments don't speak directly to fast vs. slow powder and barrel life.
Q. Does the speed of burn effect the type of recoil you feel?
Arguably yes. The overall intertia imparted to the gun will be related to the muzzle velocity of the bullet and the mass of the gaseous ejecta (e.g. from the burned powder). The more powder mass, the more gaseous ejecta. If the gaseous ejecta and bullet mass and velocity were the same for two loads, the one with the slower powder would probably feel like more of a "push" and the one with the faster powder would probably feel sharper.
In noncompensated autoloading handguns, most competitors in action sports think that a faster recoil impulse from a faster powder is faster to recover from and regain the sight picture.
Q. Accuracy?
Others have addressed accuracy to some extent. The general rule of using a powder for which the load will almost fill the case is good.
Other issues with regard to powder choice are:
. Does it meter will in your powder measure?
. Is its behavior "linear" in the region you're using it?
. Does its burn rate vary much with temperature changes?
For what it's worth, I get very consistent results from the powder measure using the Winchester ball-type powders (W748, 760), but they almost always have more velocity standard deviation and they do not reach as far as the extruded stick-type powders such as 4064, 4895, Varget, etc.
-z