What's wrong with my toilet?

Woke this morning to find a little water standing around the base of my toilet, mostly in the front. It wasn’t a lot, just enough to create a little sheen on the floor close to the toilet base. I don’t see water dripping anywhere, the floor behind the toilet is dry and so is all the porcelain that isn’t touching the floor (that is, it’s not dripping down from a crack in the bowl or something like that). Is it possible the wax ring has deteriorated somehow? Is there some other possible cause of this leak? Is it a DIY repair or will I need to call in the pros? Any idea on cost?

(FWIW, lately it’s made that occasional “running” sound and I assumed I need to replace the flapper, but just haven’t done it yet.)

Also, I’m going out of town this weekend – will it be OK if I shut off the water and fix it when I get back?