First, get backups running on production servers in an organized fashion. Just built a policy for now, then start getting things changed based on criticality.
Second, as you set things up, SCRIPT EVERYTHING. Make sure that if you setup a backup, you do so with a script so that you can deploy the same thing on other servers.
Third, get a place to test restores. Last thing you need is an explosion on production without being ready. Get this ready, practice a few restores, do log restores, point in time, get some familiarity with what’s needed on these systems.
From there, you can start to look for others test/dev servers, set up a reasonable backup strategy. If you’re not sure, post back here with specific questions in a new thread.
I would also not worry too much about all those instances. Some may be MSDE, so you might get a domain admin to query all of them and get back the results from
If you see Express or MSDE, it’s a local instance. Not worth worrying about for you.
Now, take a deep breath. This is a great chance for you to learn. Every time you think about doing something think about how to apply it to multiple servers. SQL Server has some good tools, and as you try to handle something like jobs, backups, whatever, come up with a plan. Test something on one server, make sure you have a script, and then post a new thread here, asking what others think. Then you can deploy things.