Changing wheels on bikes is harder than you might think. For starters, 26" wheels actually come in I believe three noticeably different rim sizes that are not compatible. You can tell one from the other with certainty only by their ISO numbers. Another important thing to check is the width of the new wheel from where it meets the frame on the left to where it hits the frame on the right. This is usually a semi-standard measurement such as 126mm, 130mm, or 135mm. Again - very important to get the right one. Less worrisome in my opinion is the width of the rim - some wheels are wider than others and may fit certain tires but not certain bikes.

Once you have the correct wheel, you will need special tools to change the gearing over.