Yes, you need to cycle first. Did you keep the filter pad from the other filter and add it into the tank for the BB?
If you need some good info on tank keeping, the article link in my signature is a wealth of info.
The foot print of a 10G is I believe 20" wide (x 11"), but you can go taller and have 15G tall (or 20G extra high) in the same amount of space a 10G will sit on, but you will have the advantage of 5 more gallons of course, more space to keep fish.
One of the better sizes is a 29G long, better swimming area for schooling and allows a variety of fish - 30" wide (also a 37G in a 30 wide space).
You get the idea...many more options. As well as some cube tanks, etc. for the future to consider.
If you want to keep shrimp give the tank some time to make sure it is fully cycled and stable. Be careful not to over feed the tiny little guys. Boraras Brigittae would be better to get before you get the shrimp if you are looking into fish. Then wait to make sure the parameters are stable for a month or so before adding shrimp.
It gives the tank some time to mature a little and get the biofilm /aufwuchs (microfood source) growing for tiny shrimp fry when they come about and shrimp eat it too. But you still need to feed them appropriately.
You could also look into some fish called Sundadanios (Red, Green or Blue). They like planted tank with DW and a little leaf litter for tannins and pH under ~7. They get 3/4 inch. Would work with a pair of Scarlet Gem Badis aka Dario Dario. They are a micro predator and will pick at tiny shrimp fry.
The 2 videos are from Rachel O'Leary who specializes in nano fish and also coauthored a book about them, and knows a lot about nano fish.
Red
Chilis
I have kept the Sundadanio (neon) blue they are called lots of things in the fish stores like Neon Blue Rasbora, Sundadanio Axlerodi (then the color of red, blue or green) / rasbora and they are amazinly beautiful. An unusual, not always easy to locate fish.
