I would say always go for the kill. Why? 4 kills= game. Racking up stock only improves the chances of killing. If you have the choice between kill and damage, take the kill. But his doesn't mean "don't attack unless it will kill". Damage is still beneficial, but if see a kill, take it. What was said about Squall to save Nana seems like it may be more effective, so I say try it out (I will to). What I do is Belay, then either DI away and around the lip of the edge or I Belay away from the stage and DI back. But Squall may be better because it has less lag.
Edgeguarding can be extremely painful. Like 1048576 (what the hell is with your SN?) said, it's good to mix it up. What I always do is this: if I get hit, I Smash DI and Auto-Smash DI Up so that it takes a good 150-170% to kill me. Always use WD jabs, they can lead into either a D-Smash or grab.
The combos are pretty limited, and you're going to have to play a very very mental game. Keep Ice Blocks going, Falco Laser style. The more your opponent gets hit by blocks the better chance they have of getting aggressive, and therefore messy. Blizzard/Solo Squall aren't very useful, because they have so much lag. Nairs are good, and always keep moving but watch your spacing very carefully.
As for combos....
Against fast fallers (Falcon, Falco, Fox), u-tilts, u-smashes, u-throws, and dash attacks all combo into each other very nicely and painfully
. If your opponent doesn't DI effectively you can do this:
Grab > U-throw > Dash attack > U-throw > Dash attack > D-smash/F-smash
This is a very effective and reliable zero-death combo if they don't DI. If it's not working, make sure you're jump canceling all your grabs. If it still doesn't work they're probably DIing it correctly (left or right will usually escape). Also, all fast fallers can be Chainthrown Down as long as their DI is predicted correctly. Dash attack > U-air/Nair is also effective if that first combo isn't working. Uair is preferable to the Nair in this case, as it has better combo potential.
Against medium weight characters:
(Marth, Doc, Mario, Roy, Bowser, DK, Ganon, more I'm forgetting)
U-airs are good here, they can keep them in the air for longer periods than against fast fallers. Keep wavelands or platform cancels going to so as to chase DI more effectively. Also, you can do this combo, which is quite effective, cannot be DIed out of, but is very hard to do:
Grab D-throw > Nair > Grab > D-throw..........
It's very hard to do, but with proper shuffling and spacing you can grab your opponent before they hit the ground or recover from the Nair. Best used upwards of 20% and lower than 70%.
Floaty characters:
(Samus, Zelda, Peach, Jiggs, Luigi, Kirby, again prolly forgetting some)
U-airs are your friend here, along with WD jab > Smash. The D-throw Nair works, but most characters can recover before the grab gets out. You can always jab or D-Smash though. Also, floaty characters CAN escape it with proper DI. Some of these characters you can repeatedly jab, especially at higher percents. To do this, jab, then quickly hold down. As soon as Popo crouches you can jab again. This tactic is called IASA Jabbing. IASA=Interruptible as Soon As (Frames). Another example is Link's U-smash and Pichu's taunt. IASAing is interrupting the normal lag of an attack by doing certain actions. So what you can do is jab, crouch, jab, crouch, jab, crouch, etc.. Pretty painful, and once they're at the right distance, you can get in a F-Smash, especially if you outrange them. Also, don't do this against a crouch-canceling Samus, you will get D-tilted then Baired.
Wow that turned out longer than I expected
. Good luck with your Climbers.
I'm terrible against Falcos).