I've planted a swamp cypress in mine ;-)

Try and resist the urge to rip everything out. Especially, don't go digging up any beds if you can avoid it - a lot of plants will be dormant at this time of year, so if you can, try not to disturb too much before the summer, when you may find you have a lot of plants coming up that you really like.

Meanwhile, watch the garden, see which bits get the sun, which are always in the shade. Come the summer, you may be glad of the wetness as it may mean you don't need to spend time watering.

If possible, don't try and do the whole garden at once - choose one bit to deal with, get that sorted, and when it's functioning nicely, move on to another bit. Meanwhile, the bits you're not dealing with, just keep grass mown and edges trimmed and it'll look tidy (and a lot less offensive that a bit you've dug and haven't had time to plant and which is beginningto grow a crop of weeds).

Remember too, that you can't make a garden, they need to grow, and it's in two or three years time that it'll really begin to come into its own.