Most guitar amps have an input impedance of ~1M. Lower and it can roll off the highs (not that electric guitars have much in the way of high frequency content).
I'm assuming by 'headphone amplifier' you mean a box you plug your guitar into, and headphones into, so he can hear the guitar - rather than just a headphone amp one would plug into the 'headphone out' of a guitar practice amp which isn't loud enough ?
In this instance, whilst starting off just 'making an amp' would be good, I think you should think about the possibility of adding some sort of overdrive and/or EQ.
If he's learning, then although it completely takes the fun out of DIY, there are some very nice cheap portable multieffects units about, which are pretty much designed for headphone practice, and have all manner of 'tones'. I found when learning a touch of reverb completely changed how I played, and also.. the 'nicer' tone made me play more.
As for the opamp choice, I've seen guitar outputs hit +/- 4V for the higher output humbuckers, so if running off 9V you might consider something with rail-to-rail inputs. But as you said 'jellybean' parts that makes it difficult. A TL082 is just fine for guitar (many guitar pedals use the TL072, but a TL082/4 is in quite a few, electric guitars dont' really need much bandwidth). But as you noticed, clipping might be an issue (input or output). You can always just use two 9V batteries, but I hate those things, expensive, and won't last long.