After my tank is cycled, how soon can I add some fish to it? I want to be cautious with my first ever saltwater tank! I'm trying to research and do it all right the first time instead of making mistake after mistake.....

You can add fish once the tank is cycled but do so slowly. Start with like 2 fish and test your water regularly as the fish waste will cause the water parameters to go up and you don't want elevated levels of ammonia or nitrites. After a few weeks the cycle will have adjusted to these 2 fish (you can tell because ammonia/nitrites will be at 0 when you test) and then you can add another fish or 2 and regularly test the water just like before.