Price really depends on where you live. Some areas it can be as low as $50 (this is usually with low cost clinics though), while others can be $300. The averages seem to be $150-200.
Neutering removes the testicles, which in turn eliminates the reproductive hormones. These hormones are generally responsible for behaviours such as spraying, marking, humping, circling as well as some other behaviours. It does not change the temperament or personality, and changes you see are due to the lack of those hormones. However, most people don't like being humped, sprayed and getting love dances all the time, and prefer the mellower behaviour of a neutered male.
As far as training, they may be more focused on working rather than mating. Intact males are still very trainable and can be easier if they are really focused on you.
I would say that if you have no plans for showing or breeding and just want a nice pet, then get the rabbit neutered. You won't have to deal with the behaviours and can just be happy with a nice pet who won't drive you nuts because of hormones (they will do it otherwise though).
Also keep in mind that females also have some unwanted behaviours if kept intact. They can also really want to mate and this can result in humping and tail lifting. They also tend to be more territorial and can also be aggressive especially in the cage. Some females also will spray and mark territory. Females also have a higher risk of cancer if left intact. Spaying is more expensive, usually about $25-75 more than males.