I think you are going to have to accept a certain amount of things may not work when migrated to a new machine.
But, if you have the serial number and installation for Photoshop CS6, I think that will continue to work. I ran Photoshop CS5 on Windows 10 for years and it was fine.
Your hardware specs look a little on the under-powered side. Might as well get 64 GB ram if you can afford it or at least make sure you have spare available slots to add an additional 32 if you decide to later. So if you stick with 32 GB in a four slot motherboard, get it as dual 16 GB units instead of four 8 GB that would force you to discard them if you wanted to upgrade RAM later.
You also might as well get 1 TB SSD, preferably a M.2 style one instead of SATA. The larger size gives some breathing room after all the OS and application space is used and prices aren't too much higher. M.2 gives faster performance so you might as well do that too. A four or 8 TB data drive could be another consideration. I have a couple of 8 TB drives (and a 1 TB SSD) in my current PC but I probably keep too much.
A good video card will also speed things up, and you will probably get even more performance gains if you get the new CC subscription.
At the core of it all you want a fast processor. 6 and 8 cores are pretty mainstream but for our purposes, a higher clock speed usually gives more than additional cores, although more cores is still not a bad thing.
As for your web site, I think you may want to update that anyway. There are site builder services you can subscribe to that may be able to pull the content over from the old site to make the transition easy. But if you decide to keep it, at least for the time being, it appears that you can still download Microsoft Expression Web 4 (Free Version)
here. I don't know where that would be stored locally either but it is surely there somewhere. It's also possible the application will allow you to import an existing site once you have it installed on the new PC. Services like Squarespace, Smugmug, and Zenfolio make setting a photography web site up pretty easy and they integrate the ability to sell directly too if you like. I have a site I built with Zenfolio (
www.mattb.net) that is nothing amazing and in need of an update but good enough for my needs and it looks fairly modern.
In any case, keep your old PC handy until you are sure you are done migrating. For things that do not come across well like your plugins, it's not unlikely that there is some more modern equivalent that you may need to try. So don't get hung up on a single product if some have gone by the wayside.
Good luck!
