Don't worry about the cycle unless you've got an under gravel filter. 90% or more of your bacteria is in the filter on the media, the only time that there is a truly significant amount in the gravel is if you have an under gravel filter. It needs the water flowing through it to develop a significant amount.
Pool filter sand or play sand from Lowe's, Home Depot, Ace, etc. For most standard tanks, about a pound per gallon. This is a guesstimate, you want about 1 to 1-1/2 inches. If you go with more you MUST rake through it weekly or have critters that do it for you, like Malaysian Trumpet Snails(the other MTS, lol), or you risk impaction, which can result in anaerobic gas pockets that will produce hydrogen sulfide gas, which can be instantly fatal to fish. Even with an inch and a half of sand, personally I still use MTS to stir it up, just for an added precaution.
Preparation is essential with sand. Put it in a fish safe(never had soap in it or any other fish killing nasties) bucket, fill with water a couple of inches above the sand, stir the heck out of it and pour off the "floaties". Repeat until the water stays clear or at least settles out clear quickly. If you have to do it inside, put the bucket in an old pillow case to keep the grit out of your plumbing.
Once it's in the tank, you still use a gravel vacuum to clean it but instead of digging into it, you stay above it. The debris is lighter than the sand and stays on top, a little experimentation will show you how close you can get without sucking up sand as well as fish poop and leftovers. The coarser the sand, the closer you'll be able to get, since bigger pieces of sand obviously weigh more.
As for cost, pool filter and play sand cost a lot less per pound than "aquarium" sand or gravel, but you'll probably have to buy a bigger bag than you'll need unless you can buy it by the pound if you supply the container.
Avoid argonite, crushed coral or shells. They will raise pH, and are what marine aquarium sands are made of.