Can do a HOB filter but may be good to get an adjustable one. I use an aqueon quietflow and have floating plants to create a more still area
Forgot to mention that earlier..

This filter on a 10 gallon (nice picture by the way)
[video=youtube;MA-3UmfX66Q]http://www.youtube.com/watch?v=MA-3UmfX66Q[/video]
Ive kept betta in many various tanks, I had a 12" cube that seemed about perfect size for him and ran a small hob filter with a sponge over the intake to save his long fins. I noticed mine was more active when I planted the tank and as far as tankmates, I wouldnt worry as much about the betta hurting other fish, but other fast fish can nip fins and even fast movement can stress them. Ive had luck with CPD, white clouds, ottos, pygmy cories, bristle nose plecos, snails, and especially different shrimp(yes they will eat small shrimplets especially bee shrimp and other very small ones) rams and apistos can be good tankmates if you have enough tank space. Avoid most tetras, especially neon or cardinals because ive seen them nip fins.
I have my betta in a 10 gallon. There is no filter running on it. He is about 2 years old now. He gets weekly 50% water changes and it keeps the ammonia and nitrite at zero. Only problem with not running a filter is the water develops a nasty slime coat haha.
The one I had before this one lived to be about 4 years old. Same process as this one.
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You could put him in the 5 if you want but of course 10 would be even better. Make sure it has a heater. Sponge filter should be just fine
I keep mine in a 20g long with habrosus cories and a mystery snail. They all have different personalities though, have heard of some that won't even let a snail live in the same tank as them.
Here is my baby, I can't help but to show himHe is a balloon CT.
http://i114.photobucket.com/albums/...Tank/fc7e3280-cdd0-4e5b-a14e-2708ee3226ca.jpg
I think a sponge filter would be best if you want a filter. I find that the outflow from hob filters is can be kinda strong for them. If they swim into the outflow the current takes them away because of their fins.
And as just mentioned, a heater is an absolute must.
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I have 4 betta's in my tank and they get along with everything else. They don't pick on anything but sometimes the tiger barbs can't resist the long tails on the bettas and give chase. They have plenty of leafy bush to retreat to to get away. So far their tails are still perfect, un-nipped.