Most of my generation (late 30's/early 40's) in the UK started out with Tom Duncan's excellent book, Adventures with Electronics. It's definitely old school - transistors, resistors, capacitors and (from memory) one project which used a small 3-pin IC in a radio receiver. No logic devices and definitely no PLCs. There's a follow-up, Adventures with Microelectronics and (after my time) a third book, Adventures with Digital Electronics. To me the great thing about the book was that it's divided into projects which you can just dive into - you don't need to follow the book sequentially, although it will help your understanding if you do. Every project had a written description of how it works, circuit diagrams, a layout to build it on an 'S-Dec' (solderless prototyping board) and ideas to change, improve, modify the circuit. Using the S-Dec for prototyping made it very easy to swap components to see what effect that had on the circuit's operation. All the components used were (are?) standard, unlike a lot of kits which involved daisy-chaining together proprietary modules. For a basic grounding in electronics you can't go far wrong and my son will definitely be getting my old copy and component box when he's old enough.
My advice would be to start with the basics of analogue circuits (as in the book above) and get a grounding in these things before you get into digital electronics. I have a friend who is an EE in mobile communications, at the moment 3G hardware, and he's always commenting on the lack of analogue/RF skills in the more recent EE graduates, who focus on digital. Which is good for him, as his skillset is much in demand. I'd agree with the two posters who mentioned audio/hi-fi and ham radio - hi-fi is more immediately practical in that you can make big amps etc. but there's nothing like VHF/UHF/microwave for teaching good construction skills.
Have fun and don't get too addicted to the smell of hot solder.