First off, welcome to the forum!
Quite honestly, I wouldn't recommend setting up anything under 5 gallons for a first tank. The little 1 gallon tank you posted is not going to be able to support an cycle, will need 100% water changes every few days (this can be quite tedious), and isn't big enough for really anything other than a few snails.
Because you won't be able to establish a cycle (check out this great link if you haven't read up about the nitrogen cycle: A Beginner's Guide to the Freshwater Aquarium Cycle
) a filter isn't going to do much except agitate the water a bit. Also, the ONLY filter for smaller tanks I've ever known to be completely silent is this one: Canister Filters: Rapids Mini Canister Filter at Foster & Smith Aquatics
(I used to have tanks near by bed and also hated filter noises while sleeping!).
As far as fish are concerned, you could house a single betta (male or female) in any tank over 2.5 gallon (although like I said it will be difficult to impossible to establish a cycle in anything under 5 gallons which makes frequent 100% water changes necessary). Housing multiple female bettas together isn't recommended in anything under a 10 gallon due to territory issues.
Without knowing your water parameters it is hard to recommend other fish. I would at least test for pH, ammonia, nitrite, and nitrate before buying fish. You will also need a good water conditioner that removes chlorines, chloramines, and heavy metals to condition the tank water. Most people simply use conditioned tap water for their tanks.
Hope this helped!