Welcome to the salty side.
I don't know if you're aware of this, but filters aren't typically required in saltwater tanks - the
live rock will take care of biological filtration for you, so you really just need to add flow. Most people do use some sort of mechanical filtration (like a filter sock), but it's not required. So, in your tank, you'll almost certainly want to ditch the
sponge filter for something that provides more flow. You can get some tiny, tiny
powerheads that would work, but I might recommend picking up a
HOB filter. The
Aquaclear brand is the best IMO (an AC30 would be great), but most small HOBs sized for 10-30 gallon tanks will work fine.
When you say you threw some
brine shrimp in there, do you mean you added some frozen brine for a cycle, or that you put actually brine shrimp eggs into the tank?
I'd say this tank is pretty minimum in terms of fish, but a single small clown goby should do okay as long as the tank is well-cycled and mature before it's added.
Weekly water changes will likely be a must, and it won't be the easiest tank to maintain, but it's certainly possible.