Hello! I've been keeping chickens for a couple years now and they are most definitely worth it! Fair warning, they are addicting though! We started with three and somehow worked up to about 80! We have slimmed the flock down a bit though and now only have 40 or so...
First off, what are you getting hung up about? It might be easier to address specific concerns. But for now, I'll just ramble on about what I've learned and hopefully that will help you some
Housing: You will read all different space requirements for chickens all over the internet. There is nothing
concrete because it all depends on the chickens. Some don't mind it crowded, some like a lot of space. I would say, build the biggest something you can afford, start with just 3-4 chickens and evaluate how they do by observation. If there is a lot of fighting/bickering during the day (some is normal but they shouldn't be to the point of drawing blood), they need more of a run. If they are fighting at dusk, or someone protests going to roost, they need more roost space (again, some bickering is normal but it shouldn't take them an hour to get settled).
As for building something, my boyfriend built an adorable coop out of the scrap
wood from an old pole barn. Our only cost was hardware and a package of shingles. Start looking now for things you could use as building material. Craigslist always has people giving stuff away in the free section. Be patient, free isn't usually fast but it's usually worth the wait.
As for the run, if you could fence off part of the yard, mostly to keep the dogs out, I think that would be your best bet. Some dogs can be trained to leave chickens alone but without your dogs ever experiencing chickens, you won't know how they will react until you actually have the chickens. Best not to chance it.
Food: There are lots of ways to supplement a chickens diet. They eat just about anything. I haven't quite gotten to no-cost feed but I free-range mine and right now I'm having a hard time growing food for myself much-less the chickens. Someday I'll get there. If you are unlike me, and actually have a green-thumb, it would be fairly easy to grow a majority of their diet, then you'll just have to provide a protein source.
Rooster: You absolutely don't need to get a rooster if you don't want to. There are a few benefits to having one though. A good rooster will fight off predators (mine is a big baby so he's no use there, they aren't automatically good protectors so don't rely on that). They can alert to threats, if you don't mind the crowing. I don't think it's as bad as some people say but maybe that's just me, I'll take the rooster over my peafowl anyday. From a
sustainability aspect, if you have a rooster, you technically never have to buy chickens again except maybe to bring in some genetic variance.
Predators: We have all of the things you listed here. I'll go through each one and our
experience with our free range birds;
Hawks-I believe they have taken several chicks (when with Mama hen) and possibly my bantam (very small) rooster. I have Coopers hawks attempt to pick up the full grown hens and immediately give up due to their size. I don't think they are as much of a threat unless they are of the larger variety like a Red-tailed hawk. Even then, I think they prefer smaller game.
Snakes-Only really a threat to chicks and maybe your eggs unless they are something huge like a Boa.
Raccoons-These are probably the worst, only because they are smart, persistent, and good at finding flaws in an enclosure. If you are diligent about making a secure sleeping enclosure, this shouldn't be an issue as they won't come around during the day.
Opossums-We have these around but I think they mostly just eat the dropped chicken feed. I don't think they have ever gotten any of our chickens.
Coyote- Well we never had an issue with them for the first couple years but just a couple weeks ago they managed to get 14 of our birds while we were gone. I blame this one on me though because we had to leave about an hour before sunrise and I thought "they'll be fine if we let them out early". Haven't lost any since then though.
Dogs- I don't think you mentioned this one but I thought it was important. We have had more issues with lose neighborhood dogs than anything. They think chickens are the best toys ever invented. If you have a good perimeter fence this shouldn't be an issue though.
Well I could go on but I have got to go now. If you have specific questions, I would be glad to help!