Cycling isn't as scary as it seems. As long as you have a filter AND an ammoia source - the tank will cycle. There was a sticky here that said while the tank is cycling do two 50% water changes a week and then once the cycle finishes in a month or so - cut back to one 50% a week. If you can afford the API master test kit, it would be helpful but it is not mandatory.
Do you think it would be alright to just do frequent water changes until I can get the plants and properly cycle the tank?
Like I said, if you put a filter AND a fish in there- it is going to cycle. You can do a fish in cycle - all mine were.
Would I ever change out the filter media?
Most of the bacteria you want is going to be in the cartridge -although there will be some on the tank itself, gravel and any decor you have. After a few months the cartridge is going to fall apart. And after a month the carbon will not work anymore. IMO, carbon is not necessary, it's for chemical filtration - removing odors and medicines in the water. I ONLY use carbon for the snail tank because if I dont the water will reek to high heavens in 2 days. What I do for most of my tanks is skip the cartridge and stuff it with Aquaclear filter foam - it will do mechanical and bioligical filtration. And it will last ALOT longer then the cartridge will. Every 2 weeks or so, just swish it around in old tank water to get any gunk out of it.
Also, once the tank is cycled, who do I clean it? Simply consistent water changes and gravel vacuum?
It depends on who you ask but I do a 50% water change/gravel vaccume once a week. About every 2 months or so, I remove the fish/decor and dividers and do about a 80% change and a good gravel vaccume.