It sounds like your tub is structurally supported primarily through the wood frame, as opposed to a tub with a full foam core where the foam transfers a lot of the weight directly to the base. If you look at the places the manufacturer focused on for support, you should get a very good idea how to support it under and around your deck. I wouldn't think the shell lip would be the place to support it unless the original frame supports it there.
If you decide to raise it a foot or two above your deck, there are a number of options for skirting the tub, some expensive, some a lot cheaper. I just spent almost $700 on raw redwood for a new skirt and steps for my tub. And I still have to resaw, rip, router and cut to length each piece before I start to install it. At the least expensive end you could use the same material you have for your decking and it would require just some basic tools. It could take a beating and blend well with the deck. And if your tub shell is designed for surface mount, it would make the skirt work a lot easier.
Obviously the base is important and pouring a concrete pad would be best. You shouldn't need rebar though. A simple concrete 6x6 wire mesh should work well. Just make sure you put down some 3/4" limestone or sand underneath. I would suggest a minimum of 4", though 6" would be better. Compact the sub base before pouring the concrete. If you only have black dirt when you dig out the pit, you may need to dig down to clay or sand. Black dirt is not a good base for holding weight.