Tips please for sloped muddy garden makeover ON A BUDGET!

[KidsRuinedMyLife]

We moved house over a year ago and have concentrated on the interior to begin with, however now Xmas is over it is time to turn our attention to the bog that is the back garden....

Gardeners we are not, I spent my entire twenties living in a flat, and the house we lived in afterwards had a patio garden.

So the first challenge is that the garden is sloped, UPWARDS from the back door, it has 3 different levels to it AND is north facing, so the lowest level, nearest the house, never gets any sun EVER. It's on clay, we have two dogs, the drainage isn't good, I'll leave the rest to your imagination!! If we were to patio this bit (a possibility, although may end up as gravel due to cost), where do we begin as it's so muddy?

You might need to terrace your garden. You don't say how big it is but with a hired mini-digger and some railway sleepers you should be able to level out the three levels.The dogs might appreciate artificial grass for the lower level. Give you something green but easy to clean and nicer for paws than gravel.
Second tier you could plant with some perennials suited for shade. And then the top level you might like to consider some shrubs that would stabilise the ground and suck a bit of water out of the soil so the middle and low tiers don't get water logged.
How much everything costs depends on how big your garden is and how much you're willing to do yourself. Good luck!