First off, welcome to the guild!
I just make my rivers up as I go along. I tend to put them in after other terrain features have been decided on, though sometimes I'll add a few things (why does that river curve back away from the coastline? I know! i'll add a series of hills that cuts it off!).
Other than that, it's pretty much what you just described. I'll wander them in between hill features, along the edges of (or right through the middle of) forests, as they get closer to the coasts have them a bit more windy, and occasionally (no more than once or twice in a map) toss in a delta.
I don't think i've ever had a river police citation, so I must not be entirely off base
One of the things to remember is that at when you're doing a regional map where you are showing an entire world or continent, you're often working at a scale where 1 pixel might equal 1 mile across - in that kind of situation, your rivers are more representations, as there are very few rivers out there that are a mile or more across, so realistically you would not not see many rivers at that scale if at all. Your idea of wider strokes for major rivers and thinner for smaller is a decent way to go - and if you can taper the stroke along the path so much the better, that helps the illusion of the river getting larger as more tributaries (even if you can't see them) add their flow.
If you zoom in on that region, that's when you might want to get more picky. If I want to get more precise, I'll refer to google earth (or maps) and look around till I find a region that's similar to the area I'm mapping, and look for rivers in that area to get ideas.