| Yes, the filter is one place where the bacteria grow; they also grow in the gravel and on any decorations in the tank.
You CAN get just any HOB filter large enough, but there are some that are better than others. Some have limited one or two-piece cartridges that cause you to lose some or all of your bacteria whenever you change them, and also make you always have carbon in the filter (there's some controversy about that).
Folks here usually recommend either the Hagen AquaClear or Marineland Penguin/Emperor filters. The AquaClears have separate media trays, so its easy to customize your filter media, and it's also easy to change one part without removing the part that the bacteria grow in (the foam).
The Penguin/Emperor lines have a 'bio-wheel' that provides a wet/dry home for bacteria. They come with one-piece cartridges as well, but the bigger Penguin models and the Emperor models have additional media cartridges, and there are replacement two-piece cartridges available as well. Plus, most of the bacteria live in the bio-wheel, which you don't change (just rinse in tank water if it gets dirty) so you hardly lose any.
I personally prefer the Marineland filters, but there are folks here who love their AquaClears too, and make a persuasive case for them. You really can't go wrong with either line. | 
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