How to build a safe run?

I'm new to chickens in central Indiana. We have 11 Buff Orps 10 weeks old, and it's time to let them outside. We have coyotes, coons, possums, hawks, and owls in the area. Tips for an affordable but safe run? We mapped out a 20x24' space at the edge of the woods, and we're looking at using metal T posts rather than wood, hoping they will last longer, but I haven't seen many folks use these. Do they last? Are they sturdy enough?
I read that hardware cloth is good for bottom of the run, then larger stuff (like 2x4" fence) for upper portion. We'll put the girls in the coop (a converted shed) at night but want them to be safe in the run during the day.
Also, what kind of netting/fencing would work on the top? Since we get snow, rain, occasionally hail, and because there are trees in the area (with falling leaves... and occasional limbs), I fear bird netting won't last long even though it's cheaper than "fencing" the top. What have you used that worked well? We don't want to rebuild the whole thing in a year.
I appreciate comments and help from the group! Y'all are smart! I've ready quite a few posts and am finally getting weary of researching.

These videos might help

I have the exact same question! Anybody have an answer?

Welcome to BYC from a fellow Hoosier!

You are on the right track with hardware cloth towards the bottom and larger mesh higher up. Hardware cloth will keep raccoons and others reaching through to grab your birds as well as keeping out smaller critters. One thing you didn't mention is stopping digging creature attacks. For that, you will want rocks piled around your run or some fencing extended down into the dirt to form a "skirt". Since this isn't about stopping small critters or grabbing, then larger mesh is okay here.

Make sure whatever fencing you use is well attached to any wood/posts. For example, I attached hardware cloth to wood in my coop/run first with staples, but then strengthened it with screws and washers.

Welcome!!! There are issues you need to think about first, so you can have fewer regrets (and rebuilding) later.
How safe? A chainlink dog kennel type space is useful, but it's uncovered and easy to dig under. Adding either electric poultry netting as a larger perimeter fence, or several strands of electric tape around it will deter ground predators very well. It won't keep raptors out, and without extra electric something, will be climbable, and let raccoon hands and rats and weasels in.
Tall enough to walk in is essential!
Solid roofing keeps rain and snow out and is best, if more expensive. ALWAYS consider snow load!
Safer would be a rat wall to deter digging, hardware cloth everywhere, 2"x4" woven wire over that on the lower 4', and a good dig proof foundation.
If you will lock your birds in every night without fail, you will do fine most of the time without total run security. If not, or if you really want the best, more is always better! My current coop/ run combination, right after building. It's been modified (again!) this summer, so slightly different now. Mary

If you can put a solid roof over at least part of your run, you will be very happy (and the chickens too).

I have tried all sorts of top net over my run... and had Eagles dive through them, and snow bust them down.

I am now using, and happy with, concrete reinforcing wire. When covered with chicken wire...or maybe hardware cloth for you since you are in raccoon country...it should hold up to anything. Do remember that the top wire needs to be supported by strong posts since wet snow will stick to the wire. ..snow load is heavy.