Welcome back to the Amiga world!
Looks like you unpacked it just in time before the battery could do any damage, when I got my A1200 out of the loft last June the battery in the Ram expansion had already destroyed the ram board.
Anyway no looking back now I'm half way through an A1200 Tower project, this Amiga'in is adictive stuff once you get back into it!
Check out Classic Workbench, its a great up to date workbench with lots of interesting tools and apps pre installed, I run CWB ADV SP which has the nice Glow Icons and looks just like OS3.9 even though its running on WB 3.1. Take a look
http://classicwb.abime.net/ All the best & enjoy!
Steve.