I went through this ordeal a few months ago. :-)
I didn't take notes of the process so I'll just write a few things from the top of my mind. This is what worked for me, others might have other opinions and for sure there are many ways of achieving the same result.

a) Ensure you can have both machines working for a long time. The transition will be gradual and to avoid frustrations you should be able to work in the old and check how things are organized there while you gradually build the new one. I still didn't finish this process, it's been 3 or 4 months already...

b) In the new machine, make sure you always run Vue with a right click and "run as administrator". This is absolutely vital. If you don't do this, you'll run into all kinds of trouble and it will not be obvious what it is. (There's an option to set this permanently but I never bothered to do it myself.)

c) After installing Poser and Vue, you have to bring content from the old to new one. I did things the "dirty" way: just copied everything, both Poser content and Vue content, from one machine to the other, into new folders (not over the new installation). I mean, everything. Then, both in Poser and Vue, I pointed them to the freshly copied content (in Poser as another runtime, in Vue as just another library). This generated lots of duplicated files but my time is more precious than a few GB wasted on disk.

d) Even after doing the step above, when you open a scene in Vue that you created in the old computer, chances are Vue will tell you that some texture is missing. If you want to open old scenes in the new computer, you have two options: a) the hard way, which is to tell Vue where everything is, b) the easy way, which is to save the old scene in the old computer with the option "include texture maps" and "compress". Copy the scene to the new computer and it should open fine. The problem with this "easy" way is that you have to keep the old computer running for a long time, as long as you want to open old scenes in the new computer. You can also have a mix of both methods.

e) My main work is in Vue, my work in Poser is very, very basic and I never bothered to solve the issues you talk about of opening old Poser scenes in the new Poser. If I need something, I just create it new. Maybe you should ask this at the Poser forum.

That's it, really. Very simple. It worked for me, I hope it works for you. :-)