The idea of a "starter kit" is an extremely malleable concept: If, for example, a person is not sure how keen he is on electronics it probably makes sense to start small and add more equipment and books gradually.
On the other hand, if he is sure this is something he will want to do for the rest of his life, it is more sensible to invest in really useful pieces of kit early on.
If I were starting electronics today rather than as a youngster, here is what I'd buy:
1) Tools:
i) Soldering iron 15 to 50 Watts, good name-brand.
ii) Soldering iron stand.
iii) Solder - good quality.
iv) Desoldering pump, desoldering braid or both.
v) Small pliers suitable for electronics.
vi) Small sidecutters.
vii) Wire-strippers.
viii) High-speed drill suitable for working on printed circuit boards.
ix) Drill-stand for above. - (Optional: I have used ordinary household electric drills without a stand to drill PCBs, it's just easier with the stand).
2) Test Equipment:
i) Multimeter. - Can be secondhand - good quality gear can be found on Ebay sometimes.
ii) Oscilloscope. - Can be secondhand. (If you really enjoy electronics, you'll wish you had one from day one...).
3) Components:
i) Box of resistors in variety of values used commonly. - You can buy these ready selected.
ii) Box of capacitors, as above.
iii) A few op amps. - If you are building a project which requires a particular op amp, buy a few more than needed: Frequently these can be used in other experiments.
iv) A few transistors. - As above.
v) A few diodes, both "signal" and "rectifier". - As above.
4) Circuit Construction and Development:
i) Solderless breadboard - can be useful for testing ideas before committing to final version.
ii) Copper clad FR4 boards. Either with or without photosensitve coating, depending on how you are going to build your circuits.
iii) UV exposure box. (- Only required if using photographic technique to make circuit boards).
iv) Etch-resist pen. ( Required if drawing copper traces on circuit boards by hand. Also useful for making minor adjustments to photographically produced boards, but not essential).
v) Developing chemical. (- Only required if using photographic technique).
vi) Etchant. - Ferric chloride is effective.
vii) Schematic and layout drawing software. - Eagle and Designspark are both effective, free and popular.
5) Books etc:
i) "The Art of Electronics", by Horowitz and Hill.
ii) "The Art of Electronics Student Manual", by Hayes and Horowitz. - This book provides an experimental electronics course accompanying the main text and gives advice on the sort of equipment / materials you need to obtain to complete it.
I suspect if you work through the lessons, reading the main text and doing the experiments you will learn an awful lot really quickly, much more quickly than by meandering and aimless tinkering.
iii) "Electronic Principles", by Malvino. - Extremely clear explanations and engaging prose style.
iv) Datasheets and application notes for ICs, transistors, diodes etc. - Very useful and free to be downloaded from internet.
6) Good Intro Project:
You will have to discover one yourself: What are you really interested in? - If, for example, audio interests you, you could try building a simple amplifier. If transmitters fascinate you, try building an oscillator as a start.
You might even buy a kit of some sort and build it without understanding in detail how it functions. Once you've constructed it, use the textbooks you've bought to work backwards and figure out how it works. - If you do that, you'll get some good practice soldering, if you need it, and you'll also be learning some theory.
Why not get back to us and tell us what you're interested in; maybe someone here will be able to point you in the right direction for things you can build to get started.
Hope this helps.
Analogue.