It's fine to have a filter in a 3 gallon! The tank is big enough that it's not taking up too much space, and it'll make your life a little easier. The reason people say that is because they're under the impression that you can't cycle anything smaller than 5 gallons, but that's not -completely- true. You'll be able to have a mini-cycle in the tank, so after a month or two there will be less ammonia/nitrite in your tank, but it may not cycle completely like a larger filter would allow (the limitation is that there isn't enough surface area for the bacteria... but some people have managed to get one gallon bowls to cycle). So you'll still have ammonia that you'll need to remove, whereas a full cycle would eliminate it completely.
You should be able to do 2-3 50% water changes a week (just use an airline tube for a siphon), and vacuum the substrate once every week or two since you don't have plants. Once you get plants, you don't need to do a deep substrate vacuum- just do the surface once a month. After a few weeks, you're probably going to have to start doing 3 changes consistently every week (maybe even four sometimes), but it'll level off after a little bit of bacteria gets established.
The only way to really know your water change schedule for sure is to test the water because every tank is different, but there are general guidelines.
If you get live plants, you won't have to worry about water quality much at all. They help a lot. You'd still have to change water (probably 1-2 50% a week), but they lighten the load.