There are so many schools of thought on equipment that it really depends on what your ultimate goal is.
The Germans seemed to have great success with high light, a lot of liverock, and tons of water movement. The key to this setup is tons of water movement. So for this setup, you would need a tank, live rock, sand (DSB not needed), lighting, heating, and water movement devices.
I think the above setup would be perfect for softies, znps, and lps. SPS would work if you stock it with a minimal amount of fish and do weekly water changes.
On the other hand, I tend to really love gadgets so my list will differ from everyone else's.
Going from what I think is most important to least is:
Quality test kits
Quality refractomer.
Quality RODI unit
sump
skimmer
fuge
heater
chiller
ato (kalkwasser)
controller
GFO reactor
Even with the equipment I listed, if you're willing to do 25% WC's every week, and stock fish lightly, you could get away without using a skimmer.
When I first started my reef tank, I only had an HOB refugium. I did weekly 25% WC's and the tank's parameters were always perfect.
I tend to stock my tanks with fish heavily, so a protein skimmer is a must have item.
I had gone controller-less for a while, and also debated the value of having one, but once I got one and had the opportunity to mess with it and read up on how other's use them, I was fully pro-controller. I like the fact that I can set conditional statements such as, if PH is >8.4, shut off outlet 4, then wait 1 hr and check ph levels and apply power to outlet 4 to resume top off. They also give you piece of mind that if something happens, you'll get an email alert and text telling you something is outside the range of the conditions you programmed.
Chillers are a meh type of equipment. If your house is below the temp you have the tank running at, there really isn't a need for one. My house runs rather warm in the summer even with AC, so a chiller is required.
GFO reactors I think can go either way, that's why I listed that one last. If you do WC's every week, you could probably get away with some GFO in a bag. If you're like me, and procrastinate, then a GFO reactor will give you some leeway on WC cycles. Sometimes I do them every other week, sometimes it's three weeks before I have the time and motivation to do them.
