One thing that helps hugely is an adjustable fence with some sort of setup to push the wood in against it. Bandsaw blades tend to drift, for any number of reasons; trying to move off the line of the cut. Unlike a table saw, where the fence had better be pretty well parallel to the plane of the blade, on a band saw that sort of setup can cause problems. The least of these has the blade curve outward away from the fence slightly: you don't want to see the worst.
The way around this is to have a fence that can match the drift angle of the blade. Once you set a new bade in the saw you carefully rip a piece of wood by pushing it only from one point on the back edge, and find the angle you have to feed it in to get the cut to be parallel to the edge of the piece. Once I've found this I stop the saw without removing the piece, and mark the table with tape (or, better, mark previously placed pieces of tape on the table). These marks are used to set up a tall fence that is hinged at the line of the leading edge of the saw. In theory (and often enough in practice!) feeding wood through at that angle will result in a straight cut and a flat surface. I also rigged up a set of spring loaded rollers on lever arms to hold the wood snuggly against the fence. This helps keep the wood from cupping away from the fence, due to internal stresses or the simple cussedness of the stuff. Note that if you're going to do any serious re-sawing you should check the drift angle often; it can change as the blades get dull.
Another big help I've found is a means of sharpening the blades. I set up a carriage that rides in the slot of the table to hold a Dremel tool with an abrasive cutoff wheel. This grinds off the front surface of the teeth a small amount, and restores the sharpness of the tip. It only takes about 15 minutes to touch up a blade on my 14" Jet saw with the riser block, and it ends up sharper than new. This is a decent saving with regular resaw blades that run $40 or more, and is especially helpful with carbide blades that can cost four times as much. With carbide you have to use diamond cutoff wheels, of course, but these are fairly easy to find. Eventually the blades will break, of course, but I get three or more sharpenings out of them.
The width of the blade you can use depends mostly on how rigid the frame of the saw is. Although in theory a 1" wide blade will do a better job than a narrower one, in practice that's predicated on having sufficient tension. I find on my saw that I get better results with a 1/2" or 5/8" steel blade, and have had very good luck with the 3/8" Lenox carbide blades. Carbide, of course, takes a wider kerf and wastes some wood. OTOH, a bad blade or poor setup wastes a lot more.