SQL Server – What to Do When Handed a Server for the First Time

I'm a new SQL Server DBA in a new company. Just recently, they have handed me access to the server. There are about 50 OLTP databases with different sizes, some ranging 250MB and the biggest database is 25GB with a total size of 150GB data, 100GB logs for all 50 databases.

I would like to know what could be done if you are handed out access to the instance the first time? The action plan in my head right now is to run a server-side trace and perfmon to see what's going on with the database

Is this a good plan to begin with running that server-side trace? I would like to get some insights on what to normally do in this case.

Also, they have this job that does full backup of all the 50 databases in one job every day. Is that something that needs to be separated in chunks? My thought on this one is that it's probably OK to backup all the databases in one job since the size is not that big, and still can afford to do daily full backups because of the size. (Let me know if im wrong). And according to them, they can live with the server being down for 5 days. So it seems like the RTO is very flexible.

What are the necessary things that I need to know to better perform the administration of the databases?