When I moved mine I used a 7-11 Big Gulp cup. One at a time would swim into the cup and I would gently transfer them to the bigger tank.

It worked so well and no one was stressed by a net.

I know some people just pick their fish up with their hands to transfer them. I could probably do that now but at the time my fish were not secure with being handled! Now they are.
As far as the Guppies go, I would leave them in your existing tank.
Good luck with your new tank!