That will work. You will also need a heater, a refractometer (don't get a hydrometer they are not accurate) and an assortment of test kits. Ammonia, nitrite, nitrate, phosphate, pH, calcium, magnesium and alkalinity. You only need the first three to start so you can monitor the cycle, the others can wait a few weeks till your tank is ready for fish.
The hood light will be fine. I'd get one meant for marine tanks, they have more blue in the light which will help prevent some of the algae.
I'd advise against the coral inserts. Good ones are extremely expensive. I think you are confusing live rocks with reefs. Live rock provides the majority of the biological filtration in a salt water tank. It has no special requirements for light or anything else. It provides an environment that is closer to the ocean with lots of caves the small fish that will work in a small tank. Most salt water fish are wild caught so I feel the settle in better when the environment is closer to their home. You don't need to actually buy it all as live rock. Most of mine is pukani dry rock from bulk reef supply. Costs a fraction per pound and since it is dry it weighs less per pound. I like to start with one nice piece of live rock to seed the dry. This would be what is called in the hobby Fish Only With Live Rock FOWLR.
Keep in mind once you set up the tank it will take 4-6 weeks to cycle. I'd do some searches on cycling a saltwater tank it is more involved than fresh water. Some fish stores say use a damsel fish to cycle. Don't. They are tough but the cycle is hard on any fish and it can lead to a painful death. If it survives it, they are very aggressive and will go after all other fish you add.
This Kind of leads to the next thing. Plan your fish list and run it by people who aren't going to profit from your purchase (forums not fish stores) research each fish. The order of addition is very important. Least aggressive to most aggressive. Once cycled you can only add one fish at a time and only fish that will remain small so no tangs, puffers, Angels,triggers, etc. and no mandarins or other dragonets. Live aquaria is good for listing minimum tank sizes that are fairly realistic.
While you are planning your main tank it is good to also plan a quarantine tank. Doesn't need to be much a 5-10 gallon tank ( ***** is having their dollar a gallon sale now, I think) with a hang on the back or sponge filter a small heater, and a few pieces of PVC pipe for them to hide in. This way you can quarantine all fish for 30 days of observation and treatment prior to adding to the main tank. Marine fish diseases can't be treated in the main tank. Often if they get into the tank they will kill all your fish. Leaving an infected tank that needs to sit fish less for 11 weeks so the parasites die off. Much better to never let the diseases in.