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Interest compounds so the earlier you pay the less you pay. That said, rates are currently so low you might earn more in a high rate savings account or in investments so paying off the mortgage might not be the best use of your cash. Don't underestimate how much cash you might want to keep on hand for incidentals, building work, unexpected things etc.
Mortgages are one of the cheapest loans out there so just focus on getting the best deal you can and then if you find you can afford to overpay and it makes sense, do it.
Note that afaik there is no difference between taking out a shorter term vs taking the longest term you can and overpaying to match the payments you would've made on the shorter term loan except with the longer term one you have a lower minimum payment giving you a bit of a buffer if you need it.
Circumstances can and do change.
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rhowe
Thanks @Sharkstar who do you use? Is there benefit to paying off more early on (if you can afford to) because of how interest is calculated?