Dont use a Refugium they are more harm then good. Get a sump going on the 125 because a HOB
filter or canister filter is just not needed in the SW
hobby and with few exceptions have no place in the hobby. They get packed full of waste and just create huge amounts of Phosphates and Nitrates.
Sumps can be challenging because its hard for a person to know what they really need in a sump. If I was you I would go with a super simple sump with a place for a Filter sock (only use a filter sock if you are planning on changing it or cleaning it ever 2-3 days.) A place for your skimmer that will have a constent water level regardless of how much evaporation happens, and then a double baffle to keep micro bubbles out of the Return pump section.
As far as making the transfer...well i have done this a few times and each time I have learned a little something.
#1 keeping both tanks up is ideal till you can transfer everything.
#2 Get the 125 up and running with all the stuff you got from him
#3 Dont transfer ANY sand into the new 125g buy all new sand if you want sand in the tank. (Anyone who tells you oh its fine just wash it and put it in doesnt know what they are talking about lol)
#4 Move about 20 lbs of your rock in your current tank over to the new tank. It doesnt matter if its "Live rock" or "base rock" all your rock is now live beings its in a cycled tank, All live rock means is it has an "Established" Benefical Bactria Colony.
#5 Put rock in first then new sand (if you want information on running the tank without sand let me know I have lots of good stuff about that and its what I do with all my tank)
#6 Dose the tank up to 4ppm ammonia (use pure ammonia from the store or add a few raw shrimp in a net)
#7 Test the tank till you get your Ammonia Spike, Nitrite Spike, Nitrate Spike. Ones this happens Dose the tank to 2ppm ammonia and if it converts it in 24hrs you are good to go.
#6 add two fish at a time and wait a week
#7 when all your fish are moved then move over your live rock form the other tank.
#8 When you move all your rock take a bucket of tank water from your tank and give them a good rinse you want to remove as much detris from the rocks as possible before moving them into the new tank.
#9 Dont buy a sump with Bio Balls or a Trickle Filter they are out of date and Nitrate Factories
#10 QT EVERY SINGLE FISH YOU BUY - Untill recently I have thought bah whatever who needs to qt fish. I was foolish. I just lost 900$ in fish due to Marine Velvet and this would of never happened if I would of just QT the fish for a few weeks. Also another reason is the last thing you want to do is to have to try and catch a sick fish in a 125g tank you will have to remove all your rock in order to get to them.
What kind of skimmer is it?
is the tank drilled/Have overflows?
Do you plan on a reef?
Do you mean theres two fixtures that cover 1/2 the tank each or is there two full lenght t5ho fixtures so that you have 4 bulbs over the whole system?
Also I would really suggest not using that old live rock if you dont plan on cooking it. and for the time/cost/trouble of cooking rock I would just replace the 60lbs. The rock will be PACKED full of Phosphates that will leech back into the tank and cause algae issues.
If you have any questions about what I said feel free to ask I will check back in if I see an updated post
have fun, take it slow, and enjoy the build!