Caveat: Many of these not-quite-objects produced by spells are vaguely defined and considerable DM interpretation is required. We can't use real world physics, so what sense are we to make of a mage hand that can exert a force but is not affected by other forces? If the hand can't pass through the wall of a chest, why can't I hit it with a sword? I think if I were a first level mage with the cantrip, the first test I would want to run is to dip a finger of the mage hand in a graduated cylinder to see how much water, if any, it could displace.
Why destroy when you can obliterate?
You don't have a lot of options. I agree dispel magic is your best bet, as antimagic field will only suppress the hand, not destroy it.
One other possibility is a sphere of annihilation.
The sphere "obliterates all matter it passes through and all matter that passes through it." One could argue that the spectral hand is not "matter", but there is no game definition of "matter" and the hand is a visible presence that can exert a force, so I say close enough. Further, although the hand is "spectral", a preponderance of site users believe that it is so physical as to not be able to pass through a wall or other solid barrier. If the hand can grab things and can't pass through things, I would take it to be 'matter-ish' enough for the sphere.
Further, the sphere presents its targets as either "artifacts", which are undamaged unless they say they are, or "anything else", which is "obliterated" if it fits inside the sphere. I am comfortable with the hand, not being an artifact, being considered "anything else" when given nothing more than a dichotomous choice.
or disintegrate?
Mathaddict, in a comment, suggests the disintegrate spell, which says (emphasis mine):
A thin green ray springs from your pointing finger to a target that you can see within range. The target can be a creature, an object, or a creation of magical force, such as the wall created by wall of force...
This spell automatically disintegrates a Large or smaller nonmagical object or a creation of magical force.
The hand doesn't explicitly tell us that it is a "creation of magical force", but it is certainly a magical creation. For that matter, wall of force doesn't literally say it is a "creation of magical force" either, it just says "an invisible wall of force springs into existence". If wall of force is specifically called out as affected by disintegrate, then it depends on how broadly you want to apply disintegrate's "such as" clause. As a DM, I would say the hand is close enough.
To bookend my opening caveat, these magical effects are poorly defined. After Mathaddict's suggestion, I looked up disintegrate and wall of force. But wait - if disintegrate can only target things you can see, and the wall of force is specifically invisible, how is it that disintegrate works on wall of force? Although that question was new to me, I'm not the first one to have asked it.
It is the job of the DM to decide how to rule in these cases - hopefully with an eye to either creating a world of logical rules, or one in which magic is always a mystery. Whatever you rule, it should be intentional and support your world-building efforts.