Its hard to say exactly because each reef setup is different but heres some basics...
at least 1Lb of live rock (LR) per gallon, you need to decide how deep your sand bed is going to be or you can also do bare bottom.
you will need some pretty good sized powerheads. i'm a fan of the koralias becuase they spread the water around very well so maybe 2 #5's for a 125 gallon (depends on weather its a 4' tank or a 6' 125's come both ways.
Lighting is the trickiest because it depends on what sort of corals you plan to keep in your reef.
I'd say try for something that is at least 3 watts per gallon (WPG) (there are otehr ways to measure light output but this is probbaly the easiest and fastest) so 3WPG for some nice softies like zoas, muchrooms clove polyps, xenia, stuff that like that. and much more if you prefer the harder corals you will need more like 5WPG.
T-5HO's and metal halides are very popular and LED's are getting going but still very expensive
I personally have a 4' 90 galloon tank with the nova extreme pro with individual refelctors ( individular reflectors are a must have if you go t-5HO IMO)
You will want your own RO/DI water purification system, I advise against useing tap water.
you will probably want a protien skimmer make sure you get one that is rated for at least the size of your tank or bigger. get a nice heater 300+ watts and a small backup heater is recommended.
that should do it for must have's or very populars
you could also look into a sump/refugium which helps with more water volume, air/water mixture for solid PH and a place to put all the stuff like your skimmer, heaters ect that you don't want to look at in the tank. the refugium also holds macro algae for growing copepods (fish food source) as well as getting nitrates down. can also be used if you get a fish or crab or something that is acting up it gives you a place to put it until you can decide what to do with it.
there are otehr things like canister filters, HOB filters, units for taking out phospahtes and or nitrates ect ect ect, but those are the basics.
Good luck