Oh man, Fox is so much fun offline where he doesn't have to deal with any sort of lag. Generally, you'll always want to keep moving and mix up your approaches to keep the pressure on. Fox is FAST, so that's not something to be wasted by sitting still. If you've ever booted them off the stage, go for the finisher with Bair or Shine Spikes. The shine may have gotten a range reduction, but shine spikes are still very much alive and well, and quite integral to his game.
I play defensively, so running off from attacks is a breeze with long range defense and amazing close combat skill. In fact, I do believe Fox is the fastest attacker in this game...I'm not totally sure though. Master sidesteps as well, very handy when using him. Also, the brief pause in the air given with the shine is taken for granted in a lot of cases, you can avoid juggling with it, also, if you miss a shinespike, feel free to shine again. take advantage of Fox's semi-hover ability. For combos, I find a short hopped Dair+Utilt repeated is decent, and end it off with a shine. His jab combo can be efficient if used against a wall or on a heavy character. Dtilit to Dair linked to the shine is also alright. Of course though, almost no characters have any combos anymore..