Should I use project glossaries or client glossaries or subject glossaries?
I'd advise you to use project glossaries for small in-between projects (like a flyer, letter etc.) that don't relate to your normal projects. Here, you can use project glossaries to maintain terminological consistency.
For all other projects I'd advise you to create client glossaries. If your clients work in different subject fields, you can create several subject glossaries per client.
Should I use generic glossaries besides specialised client glossaries?
Yes, I think that you should. Of course, you can get a lot of generic terms from the available MT systems very easily, but you'll notice that these MT systems don't maintain consistency between segments: here's where your generic glossary comes in.
Of course, you can use the suggestions of the MT systems to quickly create a generic glossary. They harvest the internet, you can harvest them, by creating your personal glossaries.
How do I add terms to the project glossary?
You can watch this quick and dirty movie: https://youtu.be/-nTiY3XiS3A
To add term pairs to a project glossary:
Should I enter term pairs with case as-is or in lowercase?
I advise you to enter everything in lowercase, except when:
Lenting: I'd advise you to use project glossaries for small in-between projects (like a flyer, letter etc.) that don't relate to your normal projects. Here, you can use project glossaries to maintain terminological consistency.
Wrong advice. In those cases, you can add those terms to the Project Memory (don't forget to tick Fragments when setting it up). You'll than have a "double insurance," a consistency check with both the segments and the fragments. And you don't need another resource.
Lenting: Note that with glossaries it's quite easy to change case later in a text editor (I advise Notepad++ for Windows, BBEdit on Mac). After all, glossaries are plain text files.
No need for third party apps for maintenance of TMX memories for Fragments (nor for Segments, of course).