If you want hard corals, you really do need all the main test kits. So, in addition to testing SG, pH, Ammonia, Nitrite and Nitrate, you will need Phosphate, Calcium, Alkalinity and Magnesium.
LPS tend to be hardier than SPS, so I'd start with one or two of those. Duncan's are a good call. Trachyphyllia, Acans, Euphyllia (Hammer, Torch, Frogspawn), Candy canes/Trumpets, also all have a good rep.
You need decent lighting, and LPS tend not to like strong flow (they can get torn, and will die if they do). You need to be gentle handling them too. Their soft tissue will easily get damaged against their hard/sharp skeleton if it get pressed or knocked.