Wow, funny you should mention this!
I have spent the weekend building an elevated walkway across my kitchen, and drawing up plans for an outdoor run (system of chambers and tunnels) for this BUTTHEAD CAT that we adopted last month who apparently wants to return to an outdoor lifestyle and has chosen weeks-long hunger strikes as his method of protest. (Vet bills at $800 so far, without any particularly clear sign that it's a physical problem). So we are treating it as largely, or perhaps totally, a stress issue, and so instead of rebuilding the rotting deck, re-fencing a crucial horse paddock, replacing the 80% or so of our plumbing fixtures that are not working right, or anything else useful, I am playing playground designer for this BUTTHEAD CAT.
(We do love him, but he is a BUTTHEAD, have I made this clear?
)
If you google "outdoor cat enclosures" and "outdoor cat run" you will find lots of sites with excellent photos. The do-it-yourself ones vary in how robust they are -- personally I would not use chickenwire -- but there are some great ideas. The commercial sites will make you fall over if you look at the prices, BUT contain some excellent construction ideas so are well worth viewing too.
In terms of complexity and cost, it's like chicken coops. You can do it any way you want, depending how picky you are
My suggestion is that if budget is severely limiting, see what materials you can scrounge and then say "ok what can I do with these". And yeah, you *could* probably get away just fine with chickenwire as long as it's a dogproof yard and you shut the door to the house at night to prevent exciting raccoon experiences. Although I am going to pop for 2x2 welded wire mesh instead.
Good luck, have fun, post pics!
Pat, with three perfectly good cats and one BUTTHEAD (who is at least eating well at the moment, having apparently been temporarily cured by the application of $490 to the vet's bank account)