Saltwater isn't all that much harder than freshwater, these days. In fact, I've been told that planted freshwater tanks (the ones with riotous plant growth and CO2 bubblers) can be more demanding than a reef tank. Is a saltwater tank more involved than an old-style freshwater tank with an undergravel filter? Yes, but it doesn't require a degree in Marine Biology. If you already have some experience with freshwater tanks, you'll be way ahead of the people who've never kept a tank at all.
A month sounds like a reasonable estimate to me. Some people advocate very rapid cycles, using liquid ammonia to simulate fish waste. Others will tell you to run the tank for 90 days before adding fish. What you really need to do is test for ammonia, nitrite, and nitrate while the tank is cycling. When ammonia and nitrite dwindle away to 0, and nitrate starts to rise, you can add at least one fish.
I'm not real familiar with fire shrimp, but I think a clownfish and a peppermint shrimp would be a good match. While we're talking about clownfish, keep in mind that they can live without anenomes. Keeping an anenome in a 10 gallon tank is probably not something you want to attempt on your first foray into saltwater tanks. There are many hardy soft corals and Large-polyped Stony corals (LPS) that clownfish can use as surrogate anenomes.
joeychitwood has a good point. Read, read, read, read some more, then start spending $$. Most of us don't have money to burn these days, and the more you know before you buy, the happier you'll be.