Definitely dirty but certainly salvageable. If your plan is to have an up and running tank so you don’t have to wait for it to cycle then there’s some things to keep in mind while moving a tank. If you’re wanting to start fresh (which I assume you’re not since you’re planning to keep the mushrooms) then I’d throw the sand out, dry out the rock, clean the tank obviously, acid wash the rock and start fresh. Take the mushrooms to the lfs for store credit or sell to another Reefer or ask someone to hold them for a few months. Starting fresh would be the safest way to go to ensure you’re not inheriting this other persons problems. You don’t want to start the hobby with an uphill battle.
On the other hand it “looks” salvageable for sure. To move the tank I’d take a tub for the rock, use tank water to keep wet, you can throw the mushrooms in with the rock just keep them submerged in water. Throw the sand away, never use used sand. Ditch the rest of the tank water, never use old tank water to fill the tank in it’s new location. Clean the tank and all that.
When setting it up clean the rock off as much as you can, remove as much sponge as you can and rinse the rocks off really well to remove as much detritus as possible. Then acclimate the rock and mushrooms to new salt water. Use new, clean, dry sand. Replace all mechanical filtration for new. Getting new water up to temp will help the transition go smoother for the mushroom and other inhabitants but as long as it’s room temp the heater should warm the water up fast enough to not be a huge concern. Then I’d test multiple times a day for the next two to three days for nitrates, phosphates, ammonia, pH, & Temp. After a couple days of stabilization. I’d do a follow up test for alkalinity, calcium, magnesium, pH, salinity, nitrates, phosphates, & Temp. If everything seems stable your probably good to add some more softies. Personally I run ich eradicated systems rather than ich management systems. It’s extra work and time but definitely worth it in the long run. With that being said I’d finish stocking the tank with the coral and inverts that you want and then let the tank run a fallow period (76 days with no fish) If you haven’t looked into ich here’s a good video
If you’re not wanting to go to that extent typically fish that reside in nano and pico tanks can tolerate ich pretty well anyway but some don’t... If you do want to go that route then you can still buy your fish around 6 weeks after the tank is running. They’ll be going through the QT process while the remainder of the fallow period finishes up. Then add fish accordingly to aggression. add one to two fish at a time. Test for nitrates for a few days. If they aren’t climbing then you’re good to add another. A 16 gal tank you’re not going to have more than 2-4 fish anyway...
I’d upgrade the lights to LED’s personally but you could T5’s if that’s your preference. But honestly if you’re just doing a softy tank those PC bulbs will provide enough light for now and you could upgrade later. I’d get new bulbs though if you’re going to stick with the PC’s. And one last thought, I’d replace the heater and the power head. Both are vital and both fail too often. If nothing else just replace the heater... Anyway that’s how I’d go about it. Hope that helps and gives you some food for thought. Best of luck and welcome to the hobby and R2R!!