I have just replaced the filter in my betta's tank with an air pump powered sponge filter.
I bought the sponge filter on the recommendation of the chap at the shop (yes, I know, but this was Mark at Aquatic Finatic!). He made the comment that a lot of sponge filters either stick onto the glass with a sucker or just rest on the bottom. The danger is that if one of these filters floats to the surface, they stop working. He recommended one with a weighted base, the same type they use in the shop in the betta tanks.
This is the one I have. There are two bigger ones, but nowhere does it say what size tank they are meant for. But I would say the one I have would be plenty for a 50 litre tank with shrimps.
I also bought a JBL ProSilent a50 air pump. The chap said he would go either for that one or the Aqua One equivalent. He reckoned those were the two quietest ones - though mine does hum quite loudly. It's in the kitchen so with the fridge etc also humming I don't notice it unless I listen for it. The JBL comes with a European plug so the shop included a converter plug. The box also included air line tubing and a one way valve.
I did have to buy one extra bit for mine once I started cycling it in my QT - a splitter. Basically that is a thing for attaching 2 devices to one air pump, and I use mine to bleed off some air as the current was too strong for a betta - the pump is rated for 10 to 50 litre tanks.
The other thing to bear in mind is that you can't just take the media from another, cycled filter and put that into the sponge filter. The best you can do would be to tie the mature media around the sponge and hope some bacteria migrate in to the new sponge filter. That's why I cycled mine from scratch - that and the fact I'd never done the new method of fishless cycling myself so i thought it was about time I did.