pillrushing isnt always a short hop pill, actually, I dont short hop pill very often (or I used to, I dropped doc for mario).
Pill rushing, is generall best doen with a rising pill, then a midair jump to another pill. Short hop pills can be useful sometimes, and its best to kind of mix it up.
But pills do no make or break Doc, generally, its up to you to decide whether or not you want to work pills into your game.
But totally disregarding pills is stupid, you should use them at least some of the time, but doc has other things...
The aerial neutral has decent priority, and is a nice approach to most characters, if doen correctly, it can lead to many things at low percents. A grab, up tilt, another shffl... whatever. Aerial up a is another pretty good attack, but doesnt have the usefullness that mario's has. It can help with combo's, yes, but not extensively. One thing to remember is that Doc's up tilt does not lauch up unless you got the very top of his fist in the attack, which is why if you want to combo with it, you should d throw to up tilt first. Otherwise, it can be used to outprioritize oncoming attacks, as it has really good priority.
Learn how to use f smash. It may be inferior to the fist, but it is godly good still. d throw to f smash on fast fallers at 90% is generally a death, an isanely easy death at that.
As for the fist (aerial forward a)... Alot of things can lead into a fist. neutral aerial, up aerial, up tilt, d/u throw... Anything that launches up, or not far from doc can end in a fist.
Edge guarding. mainly, you wanna camp out on the edge and wait for the right moments to aerial back a, as its pretty strong and sends them pretty much straight horizontally. Unless you're playing someone like fox, falco, CF, or g-dorf... then you want to cape. Cape can get you some insanely low percent kills...
Sidenote: dont try to play Doc like a mario. That was eventually my downfall of doc. I tried to hard to be like brown mario, when quite simply doc cannot handle the some things as mario, one main thing being the up tilt.
thats all for now... someone wanna link to my doc faq?