Wanna Be City Egg

I like the idea of starting with 3 chickens, and planting stuff they can self-harvest, and then seeing if I can add more chickens later.  One thing I am confused about: some people seem to letting their chickens into the vege garden, don't the chickens eat the veges?  If not, we have 4'x8' raised vege beds which we could put inside the chicken paddocks.

Also, in talking to some neighbours, they are paranoid about rats.  I figure my options are: 1)  to use 1"x2" fencing (for the raccoons) and a self-closing automatic feeder (for the rats), or 2) 1/2"x1/2" hardware cloth for the paddocks (on all sides and top and bottom).  It looks like 14-gauge 1x2 is priced about the same as 19-gauge 1/2x1/2, which I hope is strong enough.

Finally, how high should the paddocks be?  Remember that I am enclosing the top, so I could make it only 1 or 2 feet high, but is this enough height for the chickens to happily carouse around     The lower the height, the more places in my yard I can put the paddock (low hanging branches on fruit trees), and the cheaper it is.

Ok, I'm convinced that pastured pens are best, but I live on a city lot.  I was thinking about rotating weekly between four fixed pens, each about 60 square feet.  How many chickens could I have, so they're happy and the grass/vegetation is happy?

edit: I'm saying pen instead of paddock, because I have to enclose the top and bottom of the pen because of all the raccoons we have.

For people who have tried this system, how large a pen are you using, how many chickens do you have, and how often do you move them?

Many, many thanks!
- Peter