Is there any reason why you cannot use the original hub and simply lace it to the preferred rims?
If you must have a new hub, you should ensure that it is the correct width to fit between the rear drops. The two most common widths will be 120mm and 125mm...
You must also ensure that your present freewheel will fit the threading of the new hub. For example, you don't want to try to thread an English freewheel onto a French hub, or visa-virsa.
Also, what size wheels are on the bicycle at the moment - 700c or 27"? If 27", you might run into brake reach issues, with your present calipers having insufficient reach to meet the braking surfaces of then new rims. If that is the case, you will need to find a set of longer reach calipers.
Hope this is a help.