If you can, avoid Bitbucket. We used them for a few years and it just wasn't good, through and through.
I've been really impressed with Gitlab and we use that as a backup right now but I really think I'll be moving all of our repos over to them. Plus, you can even host your own Gitlab server.
For us it was a combination of things. It was never really service/uptime related, but I can't count the number of in-app Javascript errors or weird UI decisions they made. The issues were just not good enough and the web pages were continually slow/bloated to load.
Every time I'd open a support ticket I felt like I was a second-class citizen or that the issue I raised wasn't important to them. Continual, multiple years or bad support from them. I get that we were paying $25/mo but I just couldn't deal with it anymore.
Bitbucket dev here, I am truly sorry to hear that Mike. I've been an Atlassian for almost a decade and "legendary support" has always been something that we've prided ourselves on, so it hurts to hear about your experience! I'm not sure how long it's been, but things have hopefully improved since last time you checked out Bitbucket - the unification of Bitbucket.org with Bitbucket Server (née Stash) has meant a lot of refurbishment of the front-end code, much of which is now common across products. Our front-end and design teams have grown a lot more muscle too. If you have any specific feedback about the UI/UX I'd love to pass it on to the team.
I've been using Gitlab for a couple of years, and it's really great. Used a self hosted repo for a team of ~40, and I can't recall any major incidents or any loss of code, ever.
I actually had this happen once when I was running a small filesystem based git server. Users could login with normal shell sessions with their public key, and repo permissions were handled with the unix permissions system. Some user with a funky git UI client for windows actually deleted a repo completely from the server.
It wasn't much of an issue because of local copies, but we moved to git-shell right after that, and to gitlab not long after when then team grew beyond a handful of people.
I've been really impressed with Gitlab and we use that as a backup right now but I really think I'll be moving all of our repos over to them. Plus, you can even host your own Gitlab server.