As far as cycling goes-you'll go the first intitial one which will be the longest. But then each time you make an addition you will go through a mini-cycle which is why it is suggested you only put in one at a time with a waiting period in between to avoid a system overload. Of couse there is an exception to this rule but you'll find that out later.
The equipment you REALLY need is very difficult to determine--I can tell you right now there are a million different filters or combinations of filters that will work. But here are a few clues:
Set a budget--I mean total--that way you won't get half way and realize you can't afford the rest.
go through you're species guide books and dtermine what exactly you want to keep, like your favorite fish, the one you just have to have-- then build around him--for example you want a blue tang--ok so read up and you'll find he needs lots of room but is one of the hardier species, so you might want to splurge on a bigger tank and less on lighting which he doesn't need. Then pick his friends based on his temperment. Or let's say you a particular invert or coral you want who requires high lighting and exception water quality--spend less on the tank and more on the filter and lighting. Don't set up your system only to realize or worse don't bother to check into weather you can support what you want. Do you see what I mean???
As far as where to buy--online is the best place for me 'cause the savings are so significant--although I personnally won't buy fish on line or lr--because I'm picky I like to see exactly what I'm getting. Do a search on aquarium supplies and you'll find lots.
Yes you can put things in to cycle in fact it won't cycle at all if you don't but I recommend cycling with lr and not fish.
Sorry to be so long winded but this is one of those subjects you could just go on, and on, and on about.
remember the better thought out the system is the better and more succesful you'll be even if you don't buy top notch stuff, and the most important thing is free- PATIENCE. It is a difficult, confusing and sometimes downright maddening--but always rewarding hobby.
Good Luck
I hope this helps a little
Good Luck