I would plan on having at least a 75--and bigger will be better. That said, of course there are a number of fish that will happily live with a pair of gobies. Corals are also fine, but anemones are not a good choice--they just don't do well in most setups, and until we know more about keeping them alive for more than 6 months, they just do not belong in the average aquariasts tank.
JMO, but I think that the best tankmates for mandarins are ones that are not reef safe. Very few large fish will go after a goby--they have a thick slime coating and taste bad, so are avoided even by nippy fish and predators. I kept a very fat and happy mandarin in with a large lionfish, and small trigger and a snowflake eel with no problems. The benefit of the keeping a mandarin with these fish is that they will not compete with the mandarin for food in anyway. Another option is to have a large reef with few to no other fish--but that won't appeal to most people.
So--here are 2 options for a 75-125:
Moderate lighting--power compacts, maybe, but nothing more than that. 100+ pounds of live rock, preferably from a couple of sources. 2-4 inches of sand. Cycle the tank with about 30 pounds of base rock and a few cocktail shrimp. Once the ammonia stays at 0, add mostly cured live rock. Monitor, once nitrates are being consumed, add fish. A trigger, maybe an eel, and a small tang would be good choices. Let the tank go with these fish for 6 months. Adding a refugium with lots of coral rubble and some macro algae would be ideal, as well. Once everything is stable and you can easily find tons of pods, add the gobies.
OR
Metal hallides, with PC actinics. Same amount of live rock, plus corals. Maybe a single, reef safe fish of about 4-5 inches, and the gobies. The corals would be added once the setup cycles (same as above), then the other fish, and then the gobies.
Mandarins are actually very hardy animals. They have a reputation for being hard to keep because of their diet--very few will take to live food, but it does happen. Just don't count on it!