What tools/programs are [A] suitable for beginners [B]
powerful/flexible enough to produce quality signs?
To address what is suitable for beginners is going to be a complicated discussion because it would depend on what you find to be an issue. One would say that Illustrator would be the best suited because the amount of resources are available.
Where can I find [preferably free!] courses in both graphic design in
general, and sign-making in particular (ie, not web-design or CAD or
3D imaging....I'm not up to those...yet;)
It would be hard pressed to find "free" courses because you are basically asking someone that has put in the effort to learn design to spend their hard earned time to teach you and that simply isn't logical. Same rule applies to sign-making. However, I would suggest possibly picking up a vector program like Inkscape, that is free, and learning how to do things.
What books should I read?
That would probably depend on what program you are going to use.
Any tips for the beginner?
Expect to only get in return the amount of effort you put in. Try to come up with ways to practice in design. Don't be afraid to take advanced designs experts have done and challenge yourself in understanding what they did and the ability to replicate it. At this time you are your best client and by that I mean come up with an idea and learn how to consolidate your time and design.
Now some other points. From experience in the sign world I would advise learning a vector program since you mentioned you will be doing signs. So this tid-bit may help:
- Inkscape: Its a free vector program that has a robust community and focuses on vector.
- CorelDraw: Is another popular alternative to Illustrator that a lot of sign companies use because it can aid in the design of lighted signs and its ability to scale.
- Illustrator: One of the best vector programs that is very popular in the community and a lot of sign companies use it to develop signage and even vehicle wraps and digital prints.
- InDesign: The best print production software for stationary or small jobs when typsetting is needed.
As stated by Ryan be honest. You didn't go in detail if this position needed experience but I would imagine that any company looking for someone to handle their signs would expect some design and software knowledge of some-sort unless its an internship in their sign shop if they have one.