There is a big difference between removing old bottom paint with the intent to reapply new bottom paint as opposed to thinking you can easily remove all bottom paint and return the hull to its original gel coat look. The later being much more labor and expense. It also requires someone who knows what they are doing. If you are looking to reapply new bottom paint, the job is easier but still a pain.
Last time I priced a blasting, barrier coat and new bottom paint, the estimate was $95 a foot. I am sure its a more today.
For the DIY type, Sanding the old paint completely off may not be necessary depending on a few factors. If the previous owner kept the boat in the water for long periods (weeks and more at a time) and boats in waters similar to where you will boat and if there are no blisters, a lightish sanding and a simple primer followed by bottom paint is doable (but still a pain). As folks have mentioned, look at having someone do the job. It's worth the expense and they can also tell you what they think is necessary