John's experience almost exactly matches mine 15 years ago when I retired from teaching computer Science (basically Assembly Language Programming, and C) to undergraduates. I realised then that to keep up with advances in computing would be prohibitively expensive, so my wife suggested going back to Electronics as a hobby, as I had enjoyed being an Electrical Engineer in the 1950s. This I did, although I had only briefly met transistors, and never seen an op-amp, so I had a lot of delightful learning to do. I retained my love of Assembly Language, and when Microchip Pics appeared in the mid '90s I got hooked on them.
I can't compare them with Arduino, which I know nothing about, but an advantage of using Pics is that it is cheap to set up, as Microchip supplies all the information free, with a brilliant IDE, and you can learn to use them, as I did, from what they publish. You can start with a home-made Programmer, lots of designs on the Internet, so it would cost only a few pounds for a few Pic chips to start off with. But I would recommend the PicKit 2 which has a lot of built-in features to make program development easy. Perhaps not PicKit 3, though, see:
http://www.eevblog.com/2009/10/21/eevblog-39-pickit-3-programmerdebugger-review/ Although this has been updated, see the notes on this reference.
There is a large number of books on Pics, but some are rubbish, beware. For an easy start, an excellent introduction to Pic is:
"Designing Embedded Systems with PIC Microcontrollers: Principles and Applications" [Paperback] by Tim Wilmshurst, £22-66 on Amazon, which includes both Assembler and C. I avoided C for a while because it seemed to take away the intimacy with the hardware that Assembler gives, but with the Microchip supplied C compiler you can see the Assembler code that is generated as well.
For an overall, good, technical (not afraid to put Maths in) coverage of modern electronics I recommend: "Practical Electronics for Inventors" 2/E [Paperback] by Paul Scherz, £19-95 on Amazon.
I paid £26-99 and £22-99 respectively for these books in shops, and do not regret it at all.
I can't cover enough here, I would be happy to correspond by email on this subject: email@example.com (and, just in case, I am very wary about what I read or download or answer.)