If you're looking for a general purpose rod & reel set-up, then I would suggest a 9 or 10 wt. Either will work well, the 10 wt gives you a little more backbone & may be a better choice for larger flies in windy conditions depending on your casting experience. If you hook into smaller Tarpon, larger Snook, some of the bigger Jack's you'll have a better chance with the 10 wt. I don't feel you'll need to go heavier.
Pair the rod with a decent reel, and you'll also have a great set-up for Pike or Muskies or even Steelhead or Salmon. A spare spool is not a bad idea either, and both a floating line & intermediate line can be useful. I use both a 9 & a 10 wt for Striper & LM bass fishing. I don't need the heavy rod for the size bass I catch, but they work better due to the heavy cover & snags present in the waters I fish most. Plus, I like to throw some really big flies!
As far as brands of rods & reels, that will depend some on your budget, and there are many that will do well in saltwater. I like TFO rods, and a reel such as a Lamson Konic will work fine for general use. I have a couple of Okuma Integrity reels I use for Striped bass, but they don't make the blistering runs that some of the species you may encounter are famous for, so a better quality reel would be a good idea.
A good all around outfit of flies should include Deceivers, Clouser Minnows, Seaducers, and some topwater flies. Some of the big synthetic streamers, like those tied by Enrico Puglisi will work well too. Big poppers work well for Snook & Jacks. Rainy's makes some very good, big saltwater poppers. Gurglers & Crease flies work well on anything. As Boz indicated, some shrimp patterns are a good idea too. Anything developed by Tim Borski will be a good choice.
Get a range of flies with hook sizes from 2 up to 2/0 or 3/0. These can all be cast with a 9 or 10 wt. Colors are not extremely important in the salt, basic white, perhaps with a darker back like gray, black or olive, & chartreuse & white will work just fine. For shrimp type patterns white/pearl, tans, browns, pinks all work. Everyone you get suggestions from will have favorites, but what I've listed are good in most any saltwater situation. You should have some flies that are weighted (have a variety of weight) & some unweighted.
Your leaders don't have to be special. A basic tapered leader, with at least a 15 lb tippet is fine. 20 lb may even be better, as species such as tarpon or Snook have very sharp gill plates & can abrade line very quickly. Keep the leaders fairly short, 6 to 8 ft is good, there's not usually much need for long leaders. With an intermediate line, a shorter leader of 3 to 6 ft can work fine.
In the surf, you're going to need to control your line well, and if the leader & tippet combination is too long, you'll never know where the fly will be & it will be difficult to detect strikes & set the hook.
I know folks who use only a single strand of mono or fluoro when using an intermediate line. You might also want to have some shock tippet material in 40 to 60 lb test. A short shock tippet will be helpful in limiting abrasion if Snook or Tarpon become a primary target.
