So it's a 125 gallon reef on the 1st floor and you're going down to the sump and frag tank in the basement.....I think.....right?
125 gallons x 4 times turnover is about 500 GPH.
That's your target flow rate from the sump to the upstairs. (700 GPH if you wanna little extra margin in there...but 4x is fine.)
1" gravity drains (ie not siphons) are good for up to 600 GPH.....up to about 50% of that rate they will be silent too. Three of them gives you about 900 GPH of silent draining capacity....with some headroom. Plenty for the 500-700 GPH you'll be throwing at them.
The trick is that pumps the will deliver to the 2nd floor (could be around 16' up depending on your situation) are all pretty big compared to what your tank needs.
Mag 24, Blueline 55, Syncra ADV 10 are examples of pumps that should be a good fit.
For this flow rate you don't need big plumbing for your returns. Assuming 20 feet of return total:
- even 3/4" plumbing will only add a few feet of extra head pressure (friction loss)...about +4 ft. Fittings and pipe are SO CHEAP at this size.
- 1" will only add an extra foot or so.
- 1.25" plumbing will take friction loss to near-zero if you want to go bigger (it costs a lot more than 3/4"!).
- friction loss calculator here.
That said, Danner (ie. Mag pumps) specifies a minimum of 1.5" plumbing for the Mag 24 (and Mag 36).
If you don't mind the cost, I recommend going with 1.5" all the way to the tank....upsize the valve on the pump one size so it can flow as a full 1.5" when it's open.
There are of course lots more options for pump than what I mentioned, eg. Reeflo, Iwaki, Dolphin, etc.
As for the frag tank, it totally depends on your needs and your setup, but there's no reason to plumb it in, nor is there a reason to avoid plumbing it in – other than doing so makes things a little more complicated. (Mostly: Upsize to the Mag 36 and just make sure you have the ability to dial in the flow everywhere.)