Before you even consider touching it...are you sure? It could be the flapper just not catching the seal, and a slow stream of water slipping down the tube. Is the water in the bowl moving slightly? Fill it with a bucket of water and check for a leak...

Second, check your way backward, from the toilet to the main line. There could be another backup shutoff valve somewhere you're not familiar with.

If you don't have the slightest clue how to solder...figure it out before you get started.

That plumbing aisle is loaded with confusion for a greenhand...figure out what that pipe diameter is. Take a pic with a tape measure across it for security to hook up someone assisting you in the store.

Trigger start torch propane kit, solder, flux, pipe cutter, deburring tool, pipe brush, 2 adjustable wrenches, teflon tape, flexible toilet hose, valve, potentially a flapper kit (toilet guts), adjustable spanner wrench (I think it's called?), and I'm not 100% if that's all you need.

If you got a backup valve to work with...it looks like you could potentially pull that valve apart at the knob, and clear any blockages, before you even head out the door.