See my post here in regard to choosing your first DSLR:
https://forums.macrumors.com/threads/340242/
Now, first of all, avoid the Alpha - for a few reasons. The body itself is not designed or built too well, and it has a thunderous mirror slap. Sony's dust reduction is a joke. There is no "better" body to upgrade to (yet). The choice of lenses is quite limited, and the ones that are available are more expensive than corresponding Canon/Nikon/Oly analogs.
You father's 70s Canon lenses are FD mount manual focus lenses. They will not work with a modern EOS camera. I do not think that an adapter will be easily available, because EF and FD lenses have different registration distance.
Having image stabilization is nice - but it is by no means a "must have" feature for most common shooting scenarios.
As a rule of thumb, you need some kind of stabilization (IS, or a tripod) if you shoot with a shutter speed of 1/FL or slower (where FL=35mm equivalent effective focal length of your lens). If you shoot with a normal (50mm 35mm equiv) lens, you need to start worrying about shake if your shutter speed is 1/30s. With a 300mm telephoto you want to keep your shutter at 1/500 or faster.
Of course, this is just a rule of thumb - other things come into play here. A well-designed SLR with a properly dampened mirror mechanism has a better chance of producing shake-free images than something like, say, the Alpha
. A Leica M rangefinder camera (that has no mirror at all) with due care will allow you to shoot handheld under the conditions where you will need a tripod for any SLR.
So, in essence, you will most appreciate IS if you want to shoot a lot with long lenses and no tripod under poor lighting conditions - but you can live without it just fine.
If you want to have in-body IS, make sure to consider the Olympus E510. Not only the E510 has in-body IS - it also has an ultrasonic sensor-cleaning system that actually works, and it has live view. Also, should you want to upgrade from the kit lens, the "pro-grade" Zuiko Digital lenses are bagains in comparison to equivalent G or Zeiss T* Minolta/Sony, or Canon L lenses.
And, of course, make sure to consider Canon and Nikon - though they don't offer anything with in-body IS, and they probably won't. They do sell some expensive IS lenses instead. Canons have great high ISO performance, and in general Canon and Nikon systems are the most comprehensive, and most... entrenched
Both Canon and Nikon offer great upgrade paths.