Suggestions on cycling my new 20 gal aquarium

The goldfish are VERY small, less than one inch. I got them at
Wal-Mart over a year ago for my son who fell in love with them. I'll
have to get some pictures.

A comment about the combo, my goldfish are not aggresive, they are very
peaceful and DO NOT fight with the betta (and vice versa). They have
lived in the tank together for over 4 weeks now and both kinds of fish
have wonderful healthy looking fins. I have never heated my water and
really don't intend on buying a heater. Most of the fish I intend on
getting for this tank will be those who like temps in the 68-75
range...normal house temperature.

I have read ALOT about tank conditions on the internet and many
people/sites have commented about the ability for betta's to
comfortably live in temperature of water the range I suggested above.

Thanks for your comments Tynk, I knew there would be people (as I
already made that disclaimer) who would complain about my initial fish
combination. I do not intend on keeping the goldfish in there, that's
just all I had to work with at the time.

Can anyone make any suggestions concerning the Nitrogen numbers?