The mkII means it's the 2nd version of that machine. It has nothing to do with compatibility, it's just that both of those machines had an original version and then an update. When one gets updated again, it will be the mkIII.
I've used those CD recorders (almost 15 years ago) and they are fine. But, some time in the reasonably near future, you will start having trouble sourcing CD media. It doesn't pay to be 20 years behind the curve in digital recording.
You obviously have a computer (because you are posting here), why don't you get a cheap audio interface (probably cheaper than the CD recorder) and a free, or nearly free software package to record, edit and burn your CD's from? It's so much easier than messing with the hardware burners.
Some of the Tascam CD recorders were pretty finicky about the type of media you used. You couldn't just throw any CD-R in it and have it work.