It is fairly common to build, then tile the deck before you install the tub. You want to provide some waterproofing for that deck, since you'll probably get some splashing. Except for possibly a CI tub, you don't want to ever hang a tub by the lip, so careful measurement of the height is important. You do want it supported underneath from the floor. Note, if you build the deck a little high, you can use some mortar underneath the tub to get it the perfect height. It's possible to install the tub before you tile, but then fitting the tile under can be a big pain, and you risk getting thinset and grout on the tub...that along with getting the tile in place can scratch things...not good.
Check out www.johnbridge.com for help with this and tiling for some additional opinions.