It would really depend on the types of fish you want to keep. If you are keeping smaller, less messy fish, you can do a sponge filter as your biological filter and your weekly water changes as your mechanical filter. HOWEVER, If you are dealing with messy fish, you would be better off with a filter that combines mechanical and biological filtering or 2 different filters that will each do one of the types. ( Back in the day, we would run a filter for biological and one for mechanical so that you could totally clean out the mechanical without doing any real damage to the biological filtering.)
As for the airpump, again, it depends on the size of the tank. Just make sure that whatever size pump you get, you use a gang valve with an extra valve to release any back pressure from the pump. Back pressure will cause the pump to run hotter and make the diaphragms not last as long. I am using some air pumps still that I have had running for so long and they stopped making the parts for them years ago. THAT's the power of the gang valve
Also, you don't want a huge amount of water running through the sponges so fast so that the bacteria is spending more time hanging on for dear life rather than eating the ammonia. I run my diy sponge filters slow to medium heavy ( depending on the fish load at the time) but added a carbon chamber or bag with carbon to act as a mechanical filter to assist the filter.
Hope this helps