Is there a rule of thumb for transitions in video production?
A while back I ran some introductory video editing workshops. I used to tell the participants about a particularly cool effect that I once found in Pinnacle; it was a pinhata that came swinging into the first video along with a stick that hit the second video out of it and it unfolded across the screen.

The point of this anecdote is the following: Don't use transition presets. Like, at all. Sure it looks cool in the preview reel, but all those fancy swipes, wipes, slides et c. are just distracting and ugly. Of course it depends on what kind of video you're making, but I would always try if it works with no transitions at all first (i.e. hardcuts). If it doesn't, maybe try a simple, short cross dissolve (like, 0.5 seconds max) or maybe a dip to black. But keep your hands off all the other transition presets. 

My rules of thumb are the following:


Don't use transitions.
If you have to use transitions, use as little as possible and be consistent. 


The second point is particularly important, even if you're a fan of transitions. Be consistent with (a) what type of transition you use and (b) when you use them. For example, if you use a transition to visually seperate two scenes for the first half of your movie and then suddenly start using a transition for every cut in a scene, it's confusing and distracting. And if you drop different transitions every time, it looks like a crappy Youtube AMV made by a 12 year old. 

For example, watch Star Wars (the prequels). They use those swipes and slides with soft borders all over the place. I don't really like those, but at least they're consistent with it. 


  but some transitions between clips and stills just feel off to me


This may be opinionated, but in my experience a transition looks weird as soon as you notice it. The best possible transition is the one you don't notice, because a transition is a tool to better tell your story, not a story element itself. And the easiest way to have a transition that you don't notice is to not use one at all.