I wrote this short guide to Peggle on the GameFAQs forum in 2007.
you can shoot your first ball and through trial and error you can find out where the bucket has to be when you fire it to land it in the bucket. (i.e. Shoot the ball when the bucket is all the way to the left and if it doesn't land in the bucket, adjust slightly and try again)
Since the board always starts the same and you always shoot the same you should be able to land it in the bucket every time, giving you a guaranteed extra ball to start off with. Then you can do the same for your second shot etc. etc. to get a ton of free balls. (NOTE: This will not work well on levels with moving pegs since they will introduce random movement.)
See my video for an example: http://www.youtube.com/watch?v=uTw4Bd9yxnI
The first four or five shots are timed to land in the bucket (though I miss one).
If you aim all the way to the left of right (or you don't move the pointer at all and aim it straight down) on your first shot you can time it so that you land the ball in the bucket every time. Other than this it is hard to teach bucket strategy, you just have to make educated guesses.
The two masters I use most are Hu (the owl), Warren (the rabbit). Some levels benefit from the use of Splork (the alien) and Claude (the lobster).
Hu and Warren are all-rounders, they can be used to clear most levels easily using the zen shot or the magic hat/triple score. Splork is good for levels with big bunches of pegs, (twisted sisters, rhombi) you can clear them out in one shot with a space blast. Claude is good in the levels where the ball tends to end up on the left or right of the board, (zen frog, pearl clam, love story etc) you can use his flippers to keep your shot going for ages on certain levels.
I always aim for the purple pegs to get a point boost, then try to angle my shot so as to land in a large cluster of pegs, obviously the more orange pegs you've cleared the better as the purple will give you more points but imo it's always good to aim for them (unless they are in a horrible position obviously)
This depends of the stage/master/strategy you are using but for the most part I leave them for later on in the stage when point bonuses will be higher. Exceptions: With Claude you probably want to activate his flippers early to get the most out of them, same with Splork.
Clear all orange pegs and you get an extreme fever, buckets appear at the bottom of the board labelled 10,000 50,000 and 100,000. Depending on where the ball lands you get that many bonus points. If you clear ALL pegs (not just orange) you get an ultra extreme fever and all buckets give you 100,000 points.
I say never since you never know when you're going to get a lucky bounce and clear a level unexpectedly but if that's not your bag you should probably reset if you feel you have no chance of achieving your objective (whatever it is) rather than wasting time. Also if you have a specific strategy (i.e. resetting until you get the green pegs in a certain area or you are timing your shots to land in the bucket) you should probably reset if your strategy does not work out.
Good luck!