Some great fish to start with are sailfin mollies. Although people often buy them and keep them in freshwater, they love a little salt in their tank and a low-end brackish tank would be perfect for them. They're easy to keep and breed, and are quite compatible with brackish fish of a similar size.
I suggest you do some reading up first before you buy anything.
Here is a good link to help you get started. I also highly recommend getting
Brackish-Water Fishes: An Aquarist's Guide to Identification, Care & Husbandry , by Neale Monks.
The most basic equipment you'll need is a tank, some salt, a heater, a filter, and a hydrometer - an instrument used to measure the salinty of the water. In this case (with the mollies), you'll want to keep the SG at 1.005 or slightly below.
Once you've got the tank going and you're happy and comfortable, some good tankmates would include orange chromides and wrestling halfbeaks, provided that your tank is large enough.
Archerfish are schooling fish, and can grow to a fairly large size. As such, they'll need a tank of good proportions to house them. Stonefish are tricky, as they are difficult to get to eat most foods, and some species are known to be venemous.
After a bit of experience with the more common and hardy species, be sure to expand onto the more interesting types, as I'm sure it'll add as much excitement to the hobby like it did for me.
Good luck
SA