Firstly, as far as predators go, it is worth thinking of whether the coop will be fixed permanently in position or portable and moved every so often as this can help with deciding which vermin proofing option to take. Foxes are the biggest threat as they are sneaky, determined and will normally kill every bird rather than eat one and depart.
It would be easy for them dig under the bottom edge of this coop, especially if the ground is soft. However, sinking a coop into the ground is probably not the way to go. The timber frame would rot very quickly with moist soil always against it (a steel coop would rust). A better option would be to attach wire mesh to the bottom and secure at regular intervals to the frame with cable ties (my favourite) or tie wire. This is a relatively cheap option, easy to DIY and can be replaced when and if necessary. The coop would be secure but the chickens would not have free access to scratch the ground below. Note that if you move the coop, make sure you lift it well clear of the grass before dragging – chickens can sustain an injury if they get their feet caught in the wire while moving.
Another option if the coop is to be a permanent fixture, is to sink some wire mesh or other stronger steel mesh to a depth of around a foot the entire perimeter of the coop. This has worked with no problems for me – although it takes a bit of time, foxes will give up digging such a deep hole. The grass patch the coop is situated on will not however remain grassy for long!
The last option is securing an apron of wire mesh a foot wide to the outside perimeter of the coop and laying it on the ground. Secure with cable ties and this will deter digging and keep the portability of the pen as the mesh can be raised for moving. A good cheap option.
Check out the post called “Buying chicken pens – buyer beware” at http://www.echickenpens.com for a checklist that would be useful when considering the purchase of a chicken coop so you know you’re getting what you pay for. Good luck!