Well, a third alternative would be to use BioSpira. It instantly cycles your tank because it is wet living bacteria, nitrosomas and nitrobacter. We used this a couple weeks ago on my sister-inlaw's new tank and it did the trick. Talk about instant gratification!
If you go with the ammonia / fishless cycling method, you can add all your fish at once after the cycle is complete, but where is the fun in that? Then you have nothing else to do but look at them die one by one, among other things of course (not to say your fish would die, but you would likely be hoping a few float to the surface as you'd likely want other fish soon, and with a fully stocked tank you may find yourself hoping death on the unwanted fish).
Going with a fish-in natural cycle is what I did on my first tank a few years ago. I used one chinese algae eater, 2 corydoras, and a few bloodfin tetras. I changed a LOT of water during those first couple of months, but it was worth it as the time allowed me to think, and plan out what I wanted to do with the tank. It also gave me time to learn how to keep plants alive and thriving.
Patience is a great thing, not to be overlooked, especially in fishkeeping. For beginners who are kinda' on their own, I would always recommend a slow fish-in cycle. Take ammonia, nitrite, and nitrate readings every day or two and keep track, plotting it out on a graph (Excel works nice for this).
A ZERO nitrate reading could very well indicate your cycle has just begun, not necessarily that it is over and your tank is clean.
Then, after the cycle is complete, you have plenty of time to gradually stock your tank with the fish you want. The fish you would put in there today are very likely NOT the fish you would want to put in there in a month or two.
Patience. And patience you have. I commend you for that. I cannot tell you how many times, in the short itme I have been a member here on this forum, that I have seen a new member ask about how to set up his first tank and his signature says he has a 10gallon with 12 fish in it already, and he doesn't know squat about nitrogen. I like your signature a lot. It speaks volumes about your wisdom in the hobby. KUDOS !!!