DimitriS--First off I am going to suggest that since you have lots of questions (very good ones BTW) you REALLY need The ABC's of Reloading that I mentioned--everything you have asked about is discussed at length in that excellent volume. And getting answers from such a book is quicker than one-at-a-time over the I'net.
Re powders for .30-'06: You want a powder that pretty well fills up the case. At least 90% filling is "what to look for" but not always attainable. With large bottleneck rifle cases the powder will always more than half-fill the case, which eliminates the possibility of a double charge, a thing pistol reloaders have to concern themselves with.
'06 rounds want about a medium-speed rifle powder, and there are many to choose from. To an extent it depends on the weight of bullet you propose to use. Check in a loading manual and there will be several recipies for each bullet weight. Powder choice also depends on whether you propose to load cast lead, or jacketed, bullets: You'd use a whole different set of powders for cast than for jacketed. Some loading manuals (Nosler for one) state with which load they got the best accuracy; that is always a good place to start in your own experimenting.
Re: Speed of burning: Each powder made has a different speed of burning when ingnited by the primer. Fast-burning powders make all their pressure very quickly, and are of use in pistols where barrels are short. They also are used in shotgun loads. Very slow burning powders are used with large magnum cases and heavy bullets and long-barreled rifles, so as to push the bullet at an ever-increasing speed down the bore. There is an entire spectrum of burning speeds to choose from. In any case, "slow" and "fast" burning is a relative thing--We are talking a fraction of an instant even with the slowest of powders.
Too fast a powder is dangerous--The pressure builds up quickly, and keeps on building until the gases have somewhere to vent. If the pressure is high enough that venting will be out through the side of the barrel, ruining the gun and probably injuring or killing the shooter.
'Way too slow a powder I expect would merely result in a disappointing "Schloof!" when triggered off, and mebbe a bullet stuck in the bore. Have never read of any experimentation about this, and am not inclined to do it myself.
Anyhow, get yrself The ABC's of Reloading, and spend a couple of evenings reading it through. Krause has just put out a new edition of same--should be right up to date. www.krause.com