Setup For a 125 Gallon Reef

You've picked some hard to care for fish up there. achilles tang have a very dismal rate of survival in captivity, as do moorish idols, butterflies and anthias are not easy to keep as a whole, black tang are really rare (from my understanding), the mandarins and anemone need an established tank in order to do well in captivity, inverts won't work with some of the stocking list that you like. Pretty much would need to check compatibility with what you like before deciding and add least aggressive first to allow dominance and territory establishment. Also, some are not suitable for reef.

the equipment you listed that you weren't sure you needed, my opinion is that those might be nice down the road, but certainly are no where near essential for a successful tank. Don't forget about the live rock.

being new, I'd say that a lot of the things you want should wait a while until you are comfortable with the basics and can keep the tank with stable parameters for several months. Some would suggest 6 months to a year being stable.

Good luck with your project.

Equipment;
Re-think your skimmer choice. There are better performing models out there. Octopus and ASM top the list of 'budget' no frills skimmers that work great.

You're going to want more than 2 powerheads. Filtration in a SW tank comes from the rock and for it to be efficient you need to move the water over the rock to give the bacteria a chance to work their magic. Good flow will also keep detritus suspended so that it can be removed through your overflows/skimmer etc. It will help keep your DOC's down to acceptable levels. Koralias are a good choice though. This becomes more important if you decide to keep corals.

As for RO/DI, take a look at airwaterice.com Good products, price and support. I have the compact reefkeeper 5 stage.

Look into Eheim or Mag Drive pumps for your return. Something like a Mag9.5 would work well.

Calcium reactor isn't necessary unless you decide to keep lots of stony corals. Until then your levels will stay in check with regular water changes. You can also dose a DIY two part for Calcium and Alkalinity as an alternative to a reactor.

Ozone is also an extra associated with reefs. It keeps the water clearer for higher light penetration. With a properly designed system and good husbandry you wont see a need. I had an ozone setup on my tank last year and I saw no improvement in water clarity or ORP so I sold it.

A wavemaker is nice, but not a necessity especially if you're not keeping corals.

UV is nice to have. I don't run one so I cannot offer any recommendations here.

Livestock;

Mandarins can be tough. It's best to add them ONLY to a WELL established system. With a tank that size you'll only want to keep one because of their demands.

Maroon clowns can be very agressive. Not usually an issue in larger tanks but in a tank your size they will be very territorial.

Anthias are gorgeous fish! I will never have a reef without them. Lyretails are easy to keep if you get good specimens and feed them properly.

Any butterfly fish have STRONG tendencies to eat corals. Adding them to the tank is a gamble.

Same for angel fish. Not worth the risk.

Anglerfish and Scorpionfish, nuh uh. Best suited for agressive FO tanks.

Wrasses are awesome reef fish. Fairys and flashers stay a good size and are reef safe.

Tangs. For a tank this size I would pick three. Try to avoid pairing up fish of the same family. For example a yellow and a purple will most likely fight. A powder blue and a powder brown wont get along well. I have a powder blue, a yellow and a tomini. They all eat different types of algae and get along well.

Gobies are awesome fish. Usually not a good idea to have more than one in the tank. Just remember, if they look similar, they will fight.

Moorish idols are difficult and suited for large tanks run by experienced aquarists.

Inverts;
Take some time and put together a list of critters to make up a nice cleaner crew. Hermits, different kinds of snails, conchs and a cucumber or two.
*dwarf red legs
*scarlet reef hermits
*trochus snails
*astrea snails
*turbo snails
*sand sifting cuke(s)
*several fighing conchs

Save the clams until the tank is WELL established and you have some experience under your belt. They like stable conditoins. Something that wont come to your system for a good while.

A year from now you will have dove deeper into this hobby than you ever thought possible

Sounds like your setup is going to be great! Based upon your list I can tell you have done research and put a lot of thought into this. Great job.

Just a recommendation. I would pick a higher rated GPH return pump. I currently have a 1,100GPH return pump on my 125G and I would like to upgrade in the future. I think the rest of your flow looks good for a starting point. You could always add one more powerhead, but I don't believe that will be a major concern. I would put the money towards other things for now.

I love clowns, so I always recommend them. However, I wouldn't get a Maroon Pair. Too agressive for me. Have you thought about misbars or piscasso percs? I also like black and white ones. You might even be able to form a unique pair. Like a Black and White with a misbar/teardrop.

A cardinal pair is fun to have. They are also a very unique looking fish that attracts attention.

Royal Gramma is a good choice. Just make sure you add after the tangs.

Anthias rule! If I wasn't so cheap I would get a school.

I am sure you are familiar with the Mandarin Goby's needs. The only advice I will add is you might want to only get one, not a pair.

As for wrasses, I would only add one at most. I am only suggesting this because they can be pod eating machines. You want to avoid pod competition for a mandarin.

I wish I could help you more on the tang stocking list. But I am not familiar with all the species you listed. I do like yellow tangs though, because they colorful and usually hardy compared to most tangs.

lol I can understand the determination for a mandarin goby pair. They are beautiful fish. As long as you find ones that take prepared food then I am sure you will be fine. Although I will warn you, its very hard to find them. I always ask any time I go to the fish store. I recommend a good QT period for them. This will let you know for sure if they take prepared foods (after you watched the LFS feed them of course) and let them fatten up some more before being placed in a large time. Aggressive fish may prevent them from eating since they are shy fish.