As important as amortization is the current 'term' of the mortgage. This is the amount of time for the current conditions of the mortgage, including the mortgage lender.
In most cases, while some aspects of your mortgage may be changeable during its 'term', the interest rate and mortgage lender are not. If you want to move your mortgage to another lender (for a better deal, for instance) you will likely pay a penalty.
Mortgage terms can be as short as 6 months, or as long as 10 years. In most cases, the longer the term of the contract, the more it will cost you. Most mortgage lenders will consider a longer term to be higher risk to them - after all, interest rates could go up and that means your mortgage may not be as profitable. So, longer term mortgages will usually come with the highest interest rates.
Also, mortgage lenders want to ensure that you stay with them - after all, they are making money from your business. So, the term covers them in two ways: they insure that they make their money and that their clientele is 'stable'.