My intent is to install Linux Ubuntu 16.04 LTS, as well as Wine's latest stable version on a desktop computer. I have two of programs that I want to run on Linux, Corel PaintShop Pro 2018 (64-bit) and MAGIX Movie Edit Pro 2016 Plus.
Does anyone have any experience of running these programs on Linux?

I haven't used Wine in years.

You might start by checking Wine's application database.

As frankbell said, the Wine HQ application database is a good starting point...where both of those applications are rated as "Garbage" (that is, not functional).

If your intent is to run Linux, you'd be far better served by running native Linux apps, such as GIMP, Inkscape, Kino, Cinelerra, Blender, or any number of other apps that perform the same functions. While your performance may be OK using Wine (if you can get things to work), it sure isn't going to be as good as running it on Windows...Windows apps run better on Windows, just as Linux apps run better on Linux. Also, if you're trying to interface with video cameras or other such devices, Wine adds another layer of complexity...since there are no COM ports, and the device names are going to be different.

Thanks for the advice.
I decided to make a Windows basic installation and Linux operating system alongside. I can use PaintShopPro and Magix Video Editor in Windows and everything else in Linux.

If you're locked in to those applications, that's probably the best way to go.