Regarding acoustics...
Don't bother with the Martin Backpacker (that's the guitar in the pic you posted) if you want a slim guitar. The thing is really small, almost impossible to hold, and just doesn't feel like a real guitar. Plus, it doesn't have much of a tone, both in volume and in quality.
If you want a small guitar, there are a lot of better options. Not all full size guitars are as big as your dad's vintage Martin Dreadnought. Smaller guitars include the Seagull Grand, the Big Baby Taylor, Taylor's x12 series, and Martin's 00 and 000 models.