Covered completely is definitely best (safest, and in no way whatsoever bad for the chickens) AS LONG AS you can engineer it so it will not collapse when a) you get a foot of wet snow or b) three portly raccoons do the hungry dance up there some night. This is not necessarily quite as easy as it sounds -- you need either an actual real honest-to-gosh roof, like building a shed with no walls; or you need an almost-as-strongly-supported top of some STRONG wire mesh, i.e. NOT chickenwire. For an 11x30 run, either option (or you could do part roof and part mesh) will cost a significant bit. But if you can swing it, it is SERIOUSLY worthwhile!
It is not necessarily worth burying the foot of the run fencing, and if you DID bury it I'd suggest deeper than just a foot since most digging critters can fairly easily dig deeper than that. Have you considered an 'apron' arrangement, where you take a 2-4' wide piece of sturdy wire mesh fencing (not chickenwire) and just lay it ON the ground around the outside of the run fence, securely attached to the foot of the run fence, and the free edge pegged down or covered with rocks/pavers/turf/whatever. This is pretty much as good (except vs rats but then honestly it is almost impossible to truly keep rats out anyhow) and WAY less work in most soils
Do you
really want 7' high walls? Unless you want to leave the possibility open for someday converting a pole-barn-built roofed run into a shed for machinery or large livestock, you would save money and require a bit less seriously-engineered structure if you made the sidewalls 5-6', or even 4' if you did a peaked or shed-style roof on *rafters* rather than trusses so you still have clear headroom inside.
What wire to use is a matter of personal taste, conscience and pocketbook. The most secure thing is probably either (one can debate the merits of either
) all 1/2" hardwarecloth everywhere altogether; or heavy gauge 1x1 mesh with 1/2" hardwarecloth added on the bottom 3' of the run fence. But those things are *pricey*, especially the all-hardwarecloth option, and also the hardwarecloth is hard to see thru (you can paint it black but you will spend a lot of time *re*painting it over the years)
Definitely it is safest to have something no more than 1" mesh, ideally smaller, covering the bottom 2-3' of the run. IMHO you don't sacrifice much if any security by using 1/2" chickenwire if you can get that cheaper; even conventional 1" chickenwire is not really so bad, when being *added to* an existing secure run fence. Really, even just a decent grade of 1/2" plastic garden netting will do about 90% of what you want it to... all you are really trying to do is prevent, or slow down, "reach through" by either chickens or predators. It's a different role than your main fencing material needs to play.
For your main fencing material, if you are not going to go with the deluxe all-hardwarecloth or all-1x1-with-hardwarecloth-added models, it is just a matter of how much extra you want to pay to be HOW comfortable that strong or small-caliber predators will not get in. Some people use heavy-gauge 1x2 cage wire, which is not bad stuff at all. Some people use TIGHTLY AND CORRECTLY INSTALLED heavy gauge chainlink (but beware, there is a lot of flimsy crappy chainlink out there that dogs can just rip their way through -- and yes, much of it is sold as dog kennel panels
). If you can get heavy livestock-type 2x4 welded wire mesh, that's not really so bad IMO... weasels will slip right thru, and small baby raccoons and possums too, but if you are locking your chickens into a secure coop every day by dusk, WITHOUT FAIL, then weasels and coon/possum babies are pretty darn unlikely to be a threat. (ADULT raccoons do hunt in daytime sometimes).
I would suggest you go around to farm stores in your area, or wherever else you would get your fencing material, and price different materials. This will probably be a big factor in your decision
Things that I do not at all recommend (because they are just so easy for raccoons, dogs, coyotes etc to rip through): chickenwire of any type. That 2x2 or 2x3 wire mesh they sell as garden fencing (it is really light gauge and weak wire, and usually poorly welded too). "Corn crib" 2x4 mesh should also IME be viewed with suspicion as it seems to often have a lot of crappy welds that animals can rip apart -- but maybe it isn't all like that, I can only speak to what I've bought and seen. And anything plastic is a definite "forget it".
Note that even if you put a solid roof on your run -- which is terrific, really cuts down on mud if you do it right, etc etc -- the chickens will still get plenty of sunlight because the sun always (or, for low latitudes, "almost always" <g>) shines in at an ANGLE, same as it shines through your house windows despite having a roof on your house
Good luck, have fun,
Pat
