Seems no one wants to address the question you asked and only insist yuy get a nano cube or aqua pod. Screw those all in one outfits and go with a tank of your choice, as yu have a lot more options open up to you as well as a prodiuct thats not all proprietart and prone to cracks and other problems....That said,
Yes, yu can use LR as your main filter. It needs to be good live rock and preferably at the stocking raito of 1.25 to 1.5 pounds per gal. More is better, but it works, no it does not work, it works GREAT!.
I would still use a hob type filter as it will give you a bit more water capacity, as well as add current to the tank, and provide a plac eot put a heater or a bag of Activated charcoal etc if need be. It also provides a place in which yu can place a coarse sponge for mechanical filtration is needed....YOu can add some macro algae to this hob filter unit, and a small cheap light and turn it into a fuge pretty easy. The best hob filters for providing a hang on back fuge like this is the Aqua Clear filters...Depenidng on what sized tank yu get will determine what filter would be best. A 10 gal tanak can easily handle a AC110 filter (old model 500). 5 gal tanks wold do well with a AC70. All are easy to modify without having to buy additional parts to make them into a fuge thayt works great.
You can get a surface type skimmer that attaches to these Aqua Clear filters from the AC Mini up to the AC110 that does a fantastic job of removing the surface film.......A small pico tank (less than 5 gal IIRC) with a ACMini or AC50 w/skimmer is an awesome little setup, so is a a10 or 5 gal with the AC70 or 110 and the skimmer.......The skimmer is about $6 online.
Contrary to what everyone says, yes you can have a single goby and some shrimp in thiese small tanks. I have mainly pico tanks of 2 gal and less and each and every one have fish in them and they do just fine. I normally keep a yasha hasha goby and shrimp in one, or a yellow clown goby, citrron clown goby, black clown goby, yellow watchman goby, neon goby all do well in the small tanks....The biggest problem is keeping tank cool enough, but its sitll doable. Experiment a bait to determine how you can keep temps within reason befor e adding any fish or inverts. Yu can get retro light kits and make a hood and pack a lot of watts in a tank as small as a 1 or 2 gal capapcity or go with a 1 x 96 watt quad light by coralife with a 50/50 bulb and you can keep pretty most any thing but SPS and a few other odds and ends..........more than sufficient for a great variety......I fyur good at DIY there is a heap of stuff that can be made that will work just fine with these smaller tanks, even down to protein skimmers.....I make my own protein skimmers for my pico tanks and everything works perfect.
I would not make a sand bed any deeper than say 1" at most. Have fun, your on the right track....