My Dad built mine, and he built our family-rabbit one in 1988 (which lasted almost 20yrs), but my own joinery skills are rubbish: I can't even cut a piece of 2x4 straight :lol: I can assemble though! If you want to make your own, you will need (or be able to borrow) a decent saw, some good vices (to hold the wood), a pair of good clippers and a heavy-duty (I would recommend powered as I recall you have foxes) stapler (to attach the mesh). You may be able to get e.g. B&Q to cut the wood for you, but IIRC it's limited to a max. of 15 cuts free. Plus B&Q is more expensive than e.g. Wickes (which doesn't do free cutting IIRC).
If you do go ahead, I would recommend mitre joints reinforced with cross pieces. You might find it easier to build it in two pieces: one 'box' and one with all the fancy bits (openings) and then connect together when it's in place (permanently or otherwise depending on if you might want to move it later). Here's the 'box' end of mine part-meshed (with a Lopsy for 'scale'):
https://photos.app.goo.gl/zXoyLLZfVgcWvjf89 (I only have these on Google photos right now so can only share links, images won't work).
This one
https://photos.app.goo.gl/B3Dij1f6yviXU4Dd6 you can see the reinforcement: the cross pieces across the whole sides and in the corners. The wood used hee is very thin, not very strong at all, and I recommend you use minimum 1"x2", preferably that for the reinforcement and bigger for the main pieces.
This one
https://photos.app.goo.gl/7WBkU3vMQfGGP6tC8 shows the one that had the fold-back roof (not shown) and a fold-down panel that allows me to step into the run. The fold back roof is two part, allowing a bigger opening. It has a catch system to keep it shut. The bit under the step-through panel is where the tube goes (you can see the first half of the plywood fixed panel).
Here you can see the two parts:
https://photos.app.goo.gl/caQQMY93xfR4RHA76. The box is at the back and the complicated one at the front. They fit together so obviously that end isn't meshed
I didn't want trip/chew hazards so the only reinforcement across the floor is the end of each box.
We used 1/2"x1" weldmesh from Wickes. It doesn't have a grade and is not very strong. I can pop some of the welds myself.