Cycling a small tank like that will be difficult. Tanks that small require very frequent water changes. I'd just choose your fish and introduce it.
For my small tank, filtered, I do 100% every other day. I've seen some different suggestions around here...like 50% one week and %100 the next. It really depends on the water parameters.
Once the fish is in you can test the water frequently and set your own schedule up. However, I wouldn't be too concerned about pre cycling..
Just make sure the temperature is stable and warm enough...buy a new heater if you have to.
I'd also suggest getting a boy for no other reason then I LOVE them the most..lol. Good luck and enjoy!