I recently upgraded from a 70g to 260g so I did a little research on this and can tell you what worked for me. First, I would not reuse the existing sand and would just start over with new sand. Rinsing sand is a pain in the butt and you'll need a bunch more anyway for the larger tank. I had a bad experience with used sand before even though I rinsed the heck out of it with RO so I will never re-use sand again. In the big scheme of things, the cost of the new sand is not that much compared to everything else.
Second, will you be able to keep the existing tank running while you setup your new one? This will most likely impact how you want to do the transfer. If you have any pests or nuisance algaes now is a great time to get rid of all that mess and start fresh.
I was able to keep both tanks running when I did my transfer and took my time doing it. I setup the new tank (leak tested plumbing, installed new equipment, etc), added my additional live rock that had been curing and was "fed" for about 3 months, "fed" the new tank with a cube of mysis and checked the water over the course of a week to make sure I wasn't going to have a cycle, waited another a week to make sure, and then matched all water parameters (salinity, temp, Alk, Ca, Mg) before moving stuff over. I did not acclimate anything to the new tank and everything made it just fine.
If you cannot keep your existing tank running, consider getting a large water trough or two so that you can house your inhabitants temporarily. This will allow you to keep some water circulation going, the heater, and if you plan it right, you can still run your skimmer, keep your live rock wet, and place a light over it for corals and other photosynthetic organisms. That way, you can still have most of your filtration going and won't be in a mad rush to try to set everything up. It always seems like there is something I forgot or needed to tweak on the new tank so the extra time was welcome. Keep some prime or other ammonia lock on hand just in case things do not go as planned in terms of cycling. a 45g to 120g is a pretty big jump.
I would also make sure you have a lot of extra salt water mixed and ready to go. Even if you use some of your existing water, it will be less than you think due to volume loss from the sand bed, rock, etc. You probably won't want to use the last third or so of the water as you get closer to the sand bed and start stirring things up. No matter what happens, it always seems like you need more saltwater than you think. Personally, I would figure maybe 25 gallons of existing water will be reused from the 45 so I would go ahead and have at least a full 120 gallons ready, especially if you are not adding any new rock for now that will take up some volume. If you are getting a bigger sump, don't forget to account for the water you need for the sump. If you have leftover salt water, then just save it for your first or second water change.
