Hello there. Welcome to AA. I'm new to the saltwater world myself, but have gained a bit of experience in the FW
world. I've also done a lot of research to get my SW
put together. Here are my recommendations.
For a 50 gallon tank, your biggest hit will probably come from live rock and your skimmer. You will need 60 to 80 pounds of live rock. At about $7 to $9 dollars per pound, this is going to be the big one! However, if you are patient, you can get "dry" rock instead. It is less expensive, but it takes more time and may create an odor as it cures.
Heater - Eheim (Maybe $50)
Lighting and hood - If you aren't doing coral, then whatever you can find in your budget will work. I use T5s on both our tanks, but am leaning toward LED
2 powerheads- Hydor was highly recommended to me. These aren't too terribly expensive, but you should do some research as to how many and how powerful you need for that tank.
Protien skimmer - This will probably be one of your big ticket items for sure! I recommend Reef Octopus or Eshopps ($300... maybe more)
Air pump - Do you mean water pump? I got a "Quiet One" for about $60, but the price depends on the pump. How far will your water be traveling from your sump to your tank? That is something to consider.
Sump( what would you put in a sump?) I just used a 10 gallon tank I had for my sump. It is split into 3 sections. The first section has my skimmer, the second is full of live sand, live rock, and rubble. The 3rd section has my pump to move water back to the display.
Also, do you recommend any other equipment? I am assuming you have a drilled tank, but if not I would recommend getting it drilled. Otherwise, you will need an overflow box.
Check Amazon for some of this equimpent. You can save a ton of money on aquarium equipment there.