If you don't think you'll crash, or if you make sure to use a motor mount that won't break the motor in a crash, I'd recommend Badass. If you have a rock-solid motor mount and you're going to crash it -- Turnigy is probably the best balance of cheap and probably lasting longer than the interval between crashes.
For Kv, if you're not afraid of math, then take the pack nominal voltage, multiply it by 0.75, and write that number down. That's more or less the effective voltage you can expect on the motor at the very end of the flight when the batteries are starting to go flat. Then take your desired RPM and divide it by that number.
So, assuming 10k RPM and four cells, the voltage is (4 cells * 3.7 (volts/cell) * 0.75) = 11.1V. Then Kv = (10000 RPM) / (11.1V) = 900 RPM/volt. Choose a motor that has a Kv rating at 900 or higher.
For the current rating, you need to tell us your anticipated weight. I'm going to assume 72 ounces, because I don't know how light you build, and you just said "60 sized". I just worked this out, and I get 55A peak (for motor and ESC), and 35A average current.
Note that this 35A average current also determines the amp-hours -- 6 minutes is, conveniently, 1/10 of an hour. So 35A means 3.5 amp-hours, means 3500mA-hours. You don't want to drain the batteries dry, so you want to get something like 4000mAh in a good brand (i.e., Thunderpower), or 4500mAh in a cheap brand (i.e. Turnigy).
I have never, ever, built an electric anything that matched the pre-calculated numbers exactly. So you should use these numbers as your figures for the first few flights. If you use a charger that tells you how much charge you've put back into the batteries, then after the first five or ten flights you'll have a pretty good idea of whether you hit the battery sizing right, and you can adjust that.
Note that one of the advantages of going to a higher cell count is that as the voltage goes up, the currents (and required cell capacity) goes down. This means that your motor and battery wires get thinner, lighter, and easier to route. It also means that the individual cells can have lower capacity, so the overall pack weight stays about the same. This is why you see a lot of the "big dogs" running more cells. In a world where Thunderpower had a wider choice of pack capacities you might see more 5-cell batteries, but 6 cells is about right for a 2800mAh pack, and that's a size that Thunderpower sells, at least the last time I looked.