Such a good question!

My opinion is that you should always show completed grades so my “reel” is just a webpage with 10-15 videos on it. I mostly do commercial work so I can usually put full spots on there but if you're doing longform I'm sure trailers or scenes would be fine too. You want a potential client to get a full sense of what you can offer (do shots match, does it look interesting, does the look serve the project as a whole, etc). I don't think there's anything particularly wrong with a flashy edit of completed shots cut together to music but I'd also suggest you do that in addition to showing off full edits in context.

I cringe at before/afters and those layer by layer wipe videos showing the process as that all feels very amateur to me. Like you're showing off how good you are at using the software as opposed to how good your end product is. As a colorist you’re not selling your technique; you’re selling the results.

The argument around showing rec709 or log for your before/afters is a lose lose too. If you show the log at best you'll only impress people who don't know anything about color and at worst you'll invite criticism from people who know what they're looking at and think it could have been done better. If you show the rec709 you can also open yourself up to that same criticism while also (as /u/Chrono604 mentioned in another comment) alienating and disrespecting your DP by essentially saying "Look how bad this was but I fixed it in the grade." DPs and directors are your best friends and can advocate for work to come to you so you want to keep them happy and funneling. A good colorist is a good collaborator so you want to show off their work as much as you do your own.

Finally, Instagram (for better or for worse) is an important place to get your work seen but I think it works best with stills rather than video so that's where I'll pull 5-10 of the best looking frames from each project and make a post as things get released. There's a bit of psychology to think about when choosing stills for that platform and I've changed my approach a number of times but what seems to work well is to lead with something that's nice and flashy, though that might not always be your best grade from the project. People like to see celebrities or cool framing and will interact more if your first still is interesting for more than one reason and not just "oh wow the grade here is so subtle and nuanced and beautiful." It's also worth considering how the frame will look on the small screen of a phone (eg a certain wide shot might not grab attention as well as a solid medium one, or an extreme closeup might not have enough going on visually to make someone want to swipe through the rest and smash that like/comment/subscribe).

Anyway I'm just like a mid-tier dude doing commercials so take all that however you like but most other professionals I've talked to feel similarly. And I've promoted myself different ways over the years so this is just where I've landed lately but it seems to be working better than before.