In that case it is easy.
Get the new tank cleaned up to your satisfaction. If the filter is OK and you are happy to use the media, run it in the old tank during the clean up process.
Once you are happy put the new tank into position, put the substrate and decor in then start moving water over to the new tank from the old. It is easier to catch fish in a half empty tank. It might be easiest to remove all but the last couple of inches of water before catching the fish, as catching them will stir up muck into the water. Once the fish and as much clean water as possible is removed from the old tank add new water to fill the tank up.
As for the filter, since you don't know just how many bacteria are in the the new tank's media - it will be dependant on the amount of fish in this tank till a few days before you got it - I would use your old media because you know you have a lot of bacteria in there. Use the new tank's media to fill the spaces. Sponges can be cut up to make them fit.
If the new tank is going where the old one is now, it's a bit more complicated as you'll need to have enough containers to store all the old water and fish until you can swap the tanks around.
In the few days before the move feed the fish half rations, nothing on move day, and half rations again for a few days afterwards. You will lose the bacteria in the biofilm on the tank walls of the old tank, the substrate and any decor not being transferred. But you will gain bacteria from the filling-in bits of the new tank's media. Check for ammonia and nitrite daily after the move until you are certain they are both staying at zero.
With a bigger tank you will doubtless want more fish
Wait until everything has settled and you have had a week of double zeros. Then add more fish a few at a time. Aim for no more than a third of the fish already in the tank at one go.
I have upgraded from a 60 litre to a 125 litre, and several years later from the 125 to a 180 litre by using this method and have had no problems.