Even though the well water isn't treated with chlorine or chloramine like water from a water company, many dechlorinators will help remove heavy metals and detoxify ammonia. It's still not a bad idea to use a quality dechlorinator like Seachem Prime.
As for the filter, it unfortunately is not as simple as plopping the filter in and letting it do its thing. The usefulness of a filter is not in its ability to remove particles from the water, this makes the water look cleaner, but it doesn't remove the real danger which is something you cannot see. Every time the fish moves water over its gills, it releases ammonia as waste--kind of like the fish form of urine. This ammonia is highly toxic, any detectable level can be harmful to your fish. This is why unfiltered containers need 100% water changes.
Larger containers with filters can undergo a process in which the filter media and porous surfaces in the tank are colonized by beneficial bacteria that eat the harmful ammonia, converting it into nitrite, and then nitrate. Nitrate is much, much less toxic than ammonia, and it will not harm fish unless it is allowed to reach high levels, so once the filter is colonized, you will only have to do weekly 30%-50% water changes.
Cultivating a bacteria colony in your filter is not something that you should do blindly. It is a process that usually takes about three weeks. I always recommend purchasing a liquid master test kit like this one: http://www.fosterandsmithaquatics.com/product/prod_display.cfm?pcatid=4454
this is the only way you will know when and how much water you need to change while the bacteria colony is growing in order to provide food for the colony while keeping your fish safe. It is also the only way that you will know when the process is completed.
You should do additional research on the nitrogen cycle and how to cultivate a bacterial colony in your filter.