I know quite a bit about bucket trucks, I've owned two and have done a ton of research. The one you have shown in the photo is worthless for the most part, it's generally 29 - 32' and is a single arm with an inner boom. That was my first truck and I hated it. It has push buttons on it which is annoying because you have to hold a master button to operate causing you to use both hands to operate the controls. It's short and limited for the reach, they are usually run by generators and when it breaks your out of luck. It cost me over $2,000 to repair my generator when it broke down.
I recommend getting a double knuckle boom, they are mostly 42' except the bigger trucks are 45'. You do get more reach, but also more height and the ability to move at different angles. They have a pistol grab control which you can operate everything with one hand and it has a tension so the harder you squeeze the grip, the faster it moves and the less that you squeeze the slower. So if you want to be really careful to touch an awning or something you can move at a snails pace. With the straight booms you get speed, fast and it jerks you around.
Pay attention to rust, if the underbody is coated in thick rust, you will have major issues and repairs will cost more. I got mine from Florida and it's very clean under it.
By the way you will need an inverter so you can have 110v for drills and stuff, go with a PTO diesel if you can. Better mileage, less headaches and less noisy.
CDL is required if the truck weights more than 26,000 lbs (Class 7) As long as your truck is under that or Class 6 and below, you don't need a CDL.
As for your other questions,
- height = 42' if possible
- type of the bucket = single man is a good starter, but two man is better.
- miles on the engine = under 200,000
- generator = no
- air compressor = doesn't matter I never used mine
- should I look for it locally or on ebay? = Either is fine, just check the condition.