Your motor should be a 2 horsepower model. The motor is the heart of the belt grinder, as it will be what turns the pulleys and moves the belt that actually does the grinding. Do not skimp on the motor, opt for a model that is sealed against dust and other debris, as there will be quite a bit of it flying around once you start grinding. The motor is where the variable speed option will come in. Purchase an electric motor that can run at varying speeds, rather than one that is simply on or off.
The stand you construct needs to be strong enough to hold not only the weight of the motor and belt grinder components, but the weight of whatever material you may be grinding. If you are not an experienced welder, you may be better off purchasing a used or junked belt grinder stand and adapting it for your grinder.
Some commercial belt grinders have an additional component that is designed to pull in any dust and bits of metal that are kicked up by the grinding process. Some homemade belt grinders do not have this option, and their owners opt instead to place their grinder in a part of their workshop where cleanup will be easiest.
A 2 horsepower motor may not seem like a particularly powerful piece of equipment, but it can be extremely dangerous if it is not used properly. If you have any inclination that you are not certain of your homemade belt grinder's construction, do not use it. It is better to spend the extra money and purchase a commercial grinder than seriously injure yourself or others.