Advice For A New Senior DBA I'm finally taking the plunge and moving up from Junior DBA at a large organisation to Senior DBA at a smaller place running SQL Server. It's going to take some time for me to get a good picture of the businesses' requirements and things might be in a bit of a state as they've been without a DBA for 6 months or so. 

Is there any advice you would give to a someone starting in this position barring the things like producing a list of SQL Server instances, finding out restore point and recovery time targets, and trying to decipher what state things were left in?

Thanks!
Like you've already suggested, as soon as I got there I'd perform an inventory of all SQL Servers before then spending time running the latest version of sp_Blitz® – Free SQL Server Health Check Script and auditing the results. 

Depending on the results I'd then probably look to get in and standardise Ola Hallengrens SQL Server Maintenance Solution. You can then concentrate on running checkDB, index maintenance and getting backups offsite, security (logins, linked servers) etc.

Once the data is safe, I'd then look to either bring in a third party monitoring solution or build a basic one myself. At a minimum, I'd start capturing wait stats every minute or so.