Music

It looks like you're planning to record in there, if you're also going to be doing any mixing at all... can't recommend enough getting Sonarworks Reference. I know producers with excellent rooms who also use this software, and if your room has a lot of issues it can be a lifesaver.

Really though your absolute first port of call should be getting as much acoustic treatment as you can afford up. Bass traps in the corners, acoustic panels on the walls (if you buy ones made specifically for acoustics and cover enough space [don't forget ceiling] they will tamp down high reflections / that 'spangy' sound when you clap as a test). All your recordings will sound like a fart pushed through an onion without treatment. If it's a rental and you're worried about wrecking the paint sticking things to it, make a 'string' of acoustic panels (duct tape the string to the middle of the back of the panel), then you can put two thumbtacks in either end of a wall, tightly tie the string to each end, now you've got a row of acoustic panels with only a couple of pinpricks in the paint.

You can make a cheap 'isolator' if you want to make a vocal booth-esque thing, by draping a heavy duvet over a clothes horse, then positioning that around whatever instrument you're recording.

Is that a cheeky pair of yammies monitors I see by the door? :)