This is exactly the way I have my tank filtered.You can have a small sponge filter or a filter sock but generally the filter is actually used as a place for bacteria to grow and since you have live rock it doesn't serve any purpose other than perhaps catching bigger chunks of detritus that work their way down to the sponge.
More good ROCK SOLID information there in that one short post than you can shake a stick at. Taking it for its face value is most highly recommended. Before you progress any further forward I would suggest that you do a lot of reading and research and ask a galzillion questions here. SW tanks aint all that hard, but they are unforgiving if you make a mistake and they can certianly be pretty expensive then, not that they have to be. A good game plan will up your chances of a successful tank and few problems to deal with along the way, making it the enjoyable experience that you hoped it would be.Ok, first, you should avoid using tap water if you can help it. Also, in case you didn't you should add the appropriate amount of a declorinator which you can get at an LFS. From here on in top off the tank with deionized water which you can get in gallon jugs at a supermarket.
Second, you will do much better going to a local fish store (LFS) than to PetCo. Third, you probably don't have enough life in there from 10 lbs. of live sand to actually cycle the tank, so if you can get maybe 10 lbs. of live rock that should help get the tank going. Do you have a test kit? If not you can take a cup of water to your LFS and they will test it for you. Basically, the first spike will be ammonia, which breaks down into nitrites, then nitrates - when you have no ammonia, no nitrites and nitrates of less than 5ppm. the tank is technically cycled. In reality your tank will actually take up to a year to truly be established which is why you add animals slowly to not throw the tank out balance and start the cycle all over again.
There are lots of ways to cycle a tank, these days thankfully most people don't use fish to start the cycle, but it is still done.
I suggest that you go to an LFS and tell them what kind of tank you want to have and they can help you get going. Also, a beginners book about the saltwater hobby is highly recommended.