For me it's been my ATO and my controller!

A fat wallet!

reverse osmosis unit
skimmer
auto topoff
easyblade (algae scraper attachment for mag float, keeps the glass crystal clear and powers off coralline algae)
good lighting (figure out what corals you're interested in or plan for the future and get the best lighting you can afford ie. halides for sps/clams)

not necessarily "MUST haves" but certainly nice to have:

phosban reactor - one for phosban (phosphate remover) and one for carbon
dosing pump for calcium, alkalinity and magnesium (as your corals get larger there will be a larger demand for these and manual dosing can get tedious and expensive
controller - eventually your $10 canadian tire timer will give out and it may be at the expense of your livestock. I really like my controller, it handles everything and I can check the status of my tank remotely (temperature, pH and status of various equipment)
"fancy/pricey" powerheads - depending on the size of your tank you can get away with maxi-jets in a smaller tank but if you have the cash, spend it on a good tunze or vortech, you can often get away with one or two as they're pretty powerful and don't have to end up stuffing the tank with lots of powerheads to get the job done

oh and that too, even with buying everything used I have spent a ridiculous amount on this hobby

ATO, dosing pumps, gfo reactor, chaeto fuge.

+1 & ato

1. ATO
2. Controller
3. overized skimmer
4. LEDs
5. ROX carbon

Auto top off
Skimmer
Refugium
Lots of water movement
And lights

Fish tank, salt, water, stand, pumps, skimmer, light, pvc pipes, refractometer.

1. A tank. Preferably one that can hold water.
2. Water.
3. Salt.
4. Fish.
5. Corals.