Walmart sells 10 gallon tank for $14 the last time I checked. Pet Supplies Plus had the same price. I am sure PetSmart and Petco's prices must be close. Do not buy the package deal. I was talking about the bare tank.
What filter did you just get? Activated carbon isn't really needed. I removed my carbon pads from my canister filter a long time ago, and added more filter media into it for more biological filtration.
Yes, you can cycle with everything set up including the real/fake plants. I cycled my aquarium with full tank of real plants.
The most important thing to set up before cycling is the filter. It must run 24/7.
