So if you want to know if a certain fish you are considering will be safe in a tank with corals, that will also be displayed on the liveaquaria website. Here is an example:
http://www.liveaquaria.com/product/prod_display.cfm?c=15+38+1116&pcatid=1116
Take note of the requirements listed. That particular fish requires a tank of at least 30 gallons, is reef safe (meaning it will not harm corals), and is semi-aggressive, which means it may pose a threat to other peaceful members of the tank.
There are plenty of reef safe fish out there that you could keep in a tank with some soft corals. Introducing corals means proper lighting and a good skimmer, so be prepared to include that in your budget. You may also want to consider something like a GFO reactor and a carbon reactor, though they are not strictly necessary.
That is a good size range of tanks to start with. I would get an idea of what fish you want and what their requirements are, then let that and your budget determine what size tank to get.
Regardless of what tank you get, some essential pieces of equipment include:
Refractometer
RO/DI unit
Test Kits
Heaters
Lights
Skimmer (this can be debated, but I see it as essential regardless of what route you choose to go)
Circulation Pumps
Auto Top-Off Unit (ATO)
These are things you should absolutely plan into your budget IMO. The size an quantity of some of these items will be determined by the tank size you go with.