How can I figure out which kinds of projects/products I should try to attach myself to if I want to have a good reputation and personal brand? Correspondingly, which kinds of projects/products are best avoided?
Examples of areas might be platform teams, greenfield products, legacy codebases/products, developer tooling, products known to make money (e.g. Google Adwords), products that don't make money, projects with machine learning, reliability engineering, and so on.
Every org has folk who are hubs in the network. Info flows between groups through them. The closer you are to as many hubs as possible, the greater the chance of you being pulled into things. Getting closer to people usually means spending a whole lot of time working out what others need.
It can be as simple as lightening the mood when people are stressed, being a sounding board, solving some small issue of theirs, giving them info, helping them get connected with people who solve their issues, organizing group activities etc etc etc. The main thing is dont just do it for tech folk. You do it with sales, marketing, finance, HR, legal etc...and sooner or later you will hear about things going on even without asking. People will protect you and prop you up. Thats when you know you are becoming a hub.
Only caveat is know what your values and boundaries are. Signal them in low key way to everyone. Sooner or later either misguided ppl or total douchebags will show up and its very easy to get trapped in the wrong network.
I would as a general rule avoid anything involving being perceived as QA (stigma), or extremely speculative projects (Google+) -- because you only get one life, and keeping risk of ruin down is good. But, you may disagree and decide to go for risky things. The ROI on those is hard to calculate anything like precisely so it's more a matter of taste than math.