My league starts up next Tuesday as well...
I've read through this thread and a lot of good advice is given. The best I've ever received is...
-- Play 14.1. It will help your 8-ball game. Like 14.1, 8-ball is a pattern game.
-- Off the break, study the table for balls that have pockets to be made in, are/aren't tied up, etc. and determine the best possible out. If you break in 2 stripes and no solids, don't necessarily jump to take the stripes. The solids may be an easier out. EDIT: Unfortunately in APA, you would HAVE to take the stripes in this situation. This tip applies to where you have choice.
-- Don't always try for the out. It may not always be there. TAKE WHAT THE BALLS GIVE YOU. As others have already mentioned, leave enough balls that you can play an effective safety.
-- Play effective safeties. The idea of a safety is to gain the advantage. Don't play a safety that allows your opponent to come back with an even better one. Alternatively you can play a safety that blocks a pocket or ties up one or more of your opponents balls.
-- Don't shoot balls that obstruct the path of an opponents ball (until you have to). That may come back to haunt you.
-- And last but not least, make sure you pocket a ball on the break. I've lost my share of games breaking the balls wide open and not pocketing anything - giving my opponent an easy out.
These tips have really improved my 8-ball game.