Now is not the time for gardening in the UK, but now IS the time for removing the old fence and putting in new fencing, removing the shed (if you want it removed and I think you do) and work out where you want a patio and a new shed. Don't worry about the lawn for the time being, ignore it; it looks like it needs replacing anyway, so that's best done in March next year, and certainly not before the fencing, shed and patio are finished, it's the last thing to be done. Consider whether you still want the tree in the corner at the bottom of the garden too - not sure what it is, might be a Birch.
The first thing to do is measure it all, length and width, and take a width measurement half way down the garden as well as at the top and bottom. Draw it on graph paper, to scale, till you've got the outline of your garden, then add in things like your new shed and patio, to scale, so you can work out where best to place them. Take into account things like which way it faces (south, east, whatever) and where the sun travels - you really don't want to put a new shed in the sunniest part of the garden, though you might want a patio there.
It's hard to tell from the photo, but is the top of the garden, near the house, higher than the other end? Or the other way around? In other words, does it slope?
Fencing is the first job to get done after clearing away what's there - you might want to consider paying someone to come and erect a new fence,but you need to consider what kind of fence, what it's made of - cheap panels from Wickes or B & Q really won't last very long, so you might want to do some research into different types of fencing.
Regarding what equipment you need, depends how much of the work you're going to do yourself - if you get someone in to lay a patio, put up a fence, erect a new shed, they wil have all their own tools.
If you want to make a base for a shed you're going to erect yourself, you'll need a spade and fork (for digging), a rake for levelling, a shovel for making cement mixes, some long boards and a large piece of board (for mixing cements) plus a spirit level as a minimum. Many people mix concrete and create an oblong 'pad' for a shed to stand on (see here https://www.hanson.co.uk/en/ready-mixed-concrete/technical-information/how-to-lay-a-shed-base) but its not essential - if you work out where the edges of the shed will be after leveling the ground, its possible to just use paving slabs around the edges with a few supporting ones under the joists of the shed floor, provided you work out the spacing correctly. You will need to dig out a trench for the slabs around 6 to 8 inches deep, fill with aggregate/hardcore, then cement on top and under the slabs to keep them in place. The spirit level is essential here, along with a long, straight piece of wood to make sure they're all at the same level and each one is individually level. There are plenty of Youtube videos on how to make a shed base, so google that to find some.