A lot of my Pokemon end up with a stat-boosting move of some sort depending on their role. Dragon Dance, Quiver Dance, and Shell Smash are my favorites, but most Pokemon can't learn them, so Swords Dance and Nasty Plot are more common. I'll also sometimes use Calm Mind and Bulk Up if I can't use anything that sharply raises an attacking stat or also raise speed at the same time. Cosmic Power is also something I like to use on more defensive Pokemon, but I don't run Barrier and Amnesia as much outside of generations that don't have the Physical/Special Split.
For attacking moves, I tend to use Shadow Ball or Shadow Claw to help get unresisted coverage for stuff my STAB moves don't cover, since they're widely available and can hit almost all types for neutral damage. They're not usually my first option, but they're a solid backup especially if I have my Pokemon's attacking stat boosted by a status move. Otherwise, I usually try and find the strongest STAB move for each type that has 70+ power and 100% accuracy and matches the right attacking stat, and if I have a move leftover I use it to try and cover as many Pokemon for neutral damage as I can. There are some exceptions where I'll use a weaker move with a good side-effect, though, most notably with Normal-type moves where I almost always prefer Body Slam or Secret Power over Return for the Paralysis chance. I also prefer Rock Slide over Stone Edge, because the accuracy is much better.