Just go for fishless cycling. I do not think cycling with fish takes any shorter time in general - I did a fishy cycle and it took almost 3 months for the tank to cycle, which is longer than most fishless cycles take.
Plus if you do fishless cycling you just have to remember to add the ammonia and test the water to see what stage the cycle is at. If you are cycling with fish, you end up having to do daily (or more often) water changes so that the ammonia and nitrite don't kill the fish -- so it is a lot more work.
I don't know about adding minnows from the river - is that what you want to stock your tank with when it's all done cycling? If not, what will you do with them when your tank is done cycling? You cannot just put them back into the river - it is illegal. And if they just die in the tank while it's cycling, you'll have to get some new ones in there immediately -- if it takes you a couple days to go catch a few more, forget it, all the bacteria is dead (as there has been no ammonia in the tank to feed it) and you are starting all over again.
jm's got it right though - by far the easiest way to go is to get some used filter media from an established tank and seed your filter with that. That will give you almost an instant cycle. But, if you don't have that option, I know it's tough to be patient but I would definitely recommend a fishless cycle, which could take anywhere from 3 weeks to a couple of months.
