I have inadvertently come by a tropical tank. I've wanted one for ages and this seemed like a good opportunity, if a little grubby and uncared for. I was going to scrub it all out and start from scratch, however it transpires I have inherited some fish as well 
DH and I have managed to get the tank home and saved about a third of the water which we have put back in. I've cleaned the filter and now filter, lights and bubbles seem to be working fine. The tank however has a layer of floating crud on the bottom, and much algae on the glass.
Clearly the presence of fish means I cannot start from scratch, so what is the best way to get their tank looking shiny and fresh again? Should I top the tank up gradually over a number of days? Lots of the ornaments had been removed for transport and I've scrubbed them with a new toothbrush and hot water, but not replaced them yet, though I'm unsure if this is the right thing to do.
I have time to throw at the job and am not expecting results immediately, but would greatly appreciate advice on the best way to proceed 