Glad to see you've decided to take the step into saltwater fishkeeping. Now, lets get you started in the right direction.
The first thing you need to know is that keeping a marine aquarium is nothing like anything you've ever attempted before. When it comes to pets, if you've seen it, i've kept it. Almost every animal at the pet shop has "requirements" of care than you can bend and still successfully keep. This is absolutely not the case with a marine aquarium. You must realize up front that you simply can not attempt to push the limits or bend the "rules" you will be given for keeping a successful marine aquarium. Problems with marine aquariums occur long term, usually after 12 to 18 months, so it takes some period of time to claim success and knowledge.
Moving on...
There are also extreme differences in difficulty of fish you will see offered for sale. As a general rule, dietary needs and mature aquarium environments are the issues with success. For example, there are many Butterfly fish that are quite easy to keep in a mature aquarium environment of 150 gallons or more. However, that same fish will prove almost impossible to keep in a 55 gallon aquarium that is only 6 months old. You have to be disciplined and make smart choices in selecting fish. Every new marine hobbyist should start with "beginner" fish and VERY slowly advance into more difficult to keep species.
In the typical SMALL aquarium, you should limit yourself to 1 fish per 10 gallons of water. The fish you choose should have an ADULT size that can comfortable fit into the existing aquarium environment. It rarely works to start small and upgrade as the fish grows. Studies have shown that most marine species reach 75% of their adult size within the first year of their life. If you do not give them adequate room to grow, they will not develop properly and your success will be short lived.
For aquariums under 125 gallons in size, you should stick with Clownfish, Basslets, Gobies, Damsels, Dwarf Angelfish, small Wrasse species, some Hawkfish, and dwarf Pufferfish (if not a reef). You will not have adequate space for Lionfish, Large Angelfish, Tangs, Triggers, Groupers, large Wrasse, Butterflyfish, Eels, and other species with adult size of greater than 6''.
One of the most common beginner tanks is to choose a pair of clownfish, a single dwarf Angelfish (Coral Beauty, Flame, etc), and a Six Line or Carpenter sp. of Wrasse. This selection usually fits well in aquariums from 29 gallons to 55 gallons in size. If you move on to a 75 or 90 gallon, then consider adding a couple of goby species (Wheeler, Yellow Clown, etc.) and perhaps a Royal Gramma as well.
There are a lot of options for small aquariums, but realize going in that 90% of the fish you see at the LFS need 125 gallon aquariums or larger for long term success.