how long the tank would be fully cycled?..
hello; Sounds like you are going to do what is known as "fish in" cycling. There are other methods but this will work as long as you understand the first fish into the new tank are pretty much going to be a sacrifice. They will likely be harmed and some may die. But as you seem to think of them as future fish food already, so be it.
How to know when the tank is cycled? This is where a test kit comes in to play. Hard to say exactly how long but starting from scratch it could be weeks. When you add the sacrifice fish they will begin to add ammonia to the water and the test kit should give you a reading for the concentration.
After what may be several weeks colonies of the bb should be established and these bb should begin to convert the free ammonia to nitrites and eventually to nitrates ( Someone please correct this if I am stating the process incorrectly). When testing the water and the readings for ammonia are at or near zero, then there should be enough bb alive to consider the tank at least close to being cycled. Bear in mind there is a lot more to the process and I have left out a lot of detail.
Let me make a suggestion. You have mentioned a local fish shop. The cycling process can be sped up considerably by getting some bb loaded material from a long established tank. The bb will be on the hard surfaces in a tank such as the décor, old filter media, gravel substrate and so on. Get enough of such and you can have a cycled tank in short order.
I like snails in all my tanks and figure they will have bb colonies on their shells. The snails will also add some ammonia waste as they live in the tank. You probably need to decide about snails up front as once in a tank they can be hard to be rid of.
I like live plants and they do have a benefit. If you do not want rooted plants then the free floating type can often be had. Bear in mind that live plants may have snails as hitch hikers.