You've got a lot of good advice, but I'm going to throw in my two cents :)
It's great you want to get a 10 gallon- if you decide to, then I would check out on how to cycle
it before adding in your betta and other fish.
In a 10 gallon you could get 5 small tetras and 3-4 cories along with the one betta.. as long as you keep up on the weekly water changes which will depend whether or not you go with live plants. Also keep in mind a lot of tetras are fin nippers.. so if you don't want to risk it, you could always go with some platies, sword tails or even guppies.
A 1 gallon is a fine home for them- as long as you do the water changes each week and find a suitable heater for that size.. I would recommend a 10-15 watt. But if you are going for a 10 gallon, then a 50 watt adjustable you will want to save up for.
Filters in tanks below 5 gallons can be very strong.. I personally wouldn't use a filter in any of my 1 gallons for that reason. A filtered tank that size (or any tank under 5 gallons that is filtered) would require 2 weekly water changes of 50%- one being water only, and one being stir/dip substrate cleaning.
Personally, it's just easier to do 1 50% and 1 100% per week and not have to deal with trying to clean the substrate in such a small tank, and not have to worry about the filter. A one gallon won't hold a stable cycle- so you wouldn't have to worry about that.. anything below 5 gallons won't hold a stable cycle.
If you do decide you want to leave the filter in, then you can get an aquarium sponge and cut it to fit into the outflow section- held on by a new/clean rubber band. That should reduce the flow from the filter.. but in a 1 gallon you will always have some current at the surface.