I am happy to help! So, first things first I can't go any farther with out saying that the tank you have picked out is very small and can be kinda hard to keep, the salinity can be hard to maintain. But I don't want to discourage you, its a great place to start and maybe one day you will be maintaining a bigger tank. But anyways here is how I see the different types of coral,LPS stands for Large Polyped Stony, LPS is one of the 3 main types of corals. The name gives a decent description of the coral but I like to describe them as the fleshy corals with a calcified base because not all LPS corals have long polyps/tentacles such as Euphyllia (Frogspawn/ Torch/ hammer) and are more fleshy and don't have their tentacles extended at all times like other LPS, Examples of these include Acanthastrea, Cynarina, brain coral, blastomussa and chalice coral. SPS coral stands for short polyped stony, SPS is in my opinion, the hardest coral to keep because most SPS requires near perfect water conditions and high lighting but in case you are interested in the types of SPS here are some species of SPS: Acropora, Seriatapora, Hydnaphora, montipora, pavona and stylophora. Also, these types of corals have a calcified skeleton, just look these up on the internet most types of SPS are very stunning but most corals are very stunning. And last but not least, probably the easiest type of coral to care for soft corals, this type of coral does not have a skeleton, this includes all of your zoas, palys, mushrooms, xenia, GSP, and kenya trees. For you, I suggest you stay away from the SPS as you don't have the kind of lighting to maintain the health of SPS. I think you should start out with discosoma mushrooms as these are the hardiest of corals and almost impossible to kill, these come in many vibrant colors. Also, if you are to even try to keep a fish in a 5 gallon aquarium, I suggest that you preform weekly water changes of 1-2 gallons of water. For your tank I think that a clown goby would be perfect as they don't get above an inch, another good suggestion for the stocking is maybe a fire fish but you will need to keep a lid on your tank as these fish are prone to jumping. Personally I wouldn't keep a fish in that size of tank but this is your tank and therefore your choice. The best corals for you to get would be discosoma, zoas/palys, maybe Acanthastra, sinulara(soft coral), and a type of leather coral. Remember not to go crazy when stocking your tank, you have a small tank and should respect the fact that you don't have all that much room. Speaking of which when buying corals, always buy frags, they are cheaper than whole colonies and will grow out in time. You can even find out when the next local frag swap is in your area and the swaps usually have a great selection of corals from other reef keepers at a lower price than what a lfs you sell you. As for shrimp, I suggest a skunk cleaner shrimp or a fire shrimp as these are both very beautiful and are generally easy to take care of and reef safe. Never buy peppermint shrimp as they can be labeled reef safe but aren't (I have had trouble with this before). When buying from the lfs, don't let the person whom comes to help you talk you into something you don't want or can't take care of (they have tried to do this before). As for your filtration, that should be good enough to take care of a couple pieces of coral and a shrimp... Maybe a fish but you know how I feel about fish in a tank that size but again it is your decision. Something I forgot to mention was that soft corals and lps generally don't need that high of lighting, which is why I have recommended them to you. Also, I need to correct myself from my previous message, for a 5 gallon tank, you would need 5-7.5 lbs of rock. Every tank needs a clean up crew, so you should be getting some snails and hermit crabs and if you choose to I wanted a star when I started and I ended up losing a $50 anemone to one of his meals. Please forgive me for jumping around so much.
If you have any more questions, please ask, I enjoy helping out with tank builds!
~Sean