Welcome to BYC!

Great to have you here!
I live in an area like that too - every kind of predator and wildlife you can imagine (although, no elephants or tigers, LOL!) and I use a secure coop and covered run. My neighbors make fun of me, too, but I don't mind.

I sleep well at night and when I get up in the morning the whole crew is still there.
Put a little thought into building your coop. Mine has a cement floor. NOTHING is going to dig in through that. Build well and strong. The other benefit is you won't have to constantly be fixing it. Build a large run, secure it well and cover it with netting. That way, instead of posting a thread about how there are hawks in you area and what should you do, you can simply get out your bird books and enjoy them.
There are those who free-range and it works for them, although most will admit you must accept some losses. I'm trying to breed certain chickens, so for me, it's really hard to lose even one. For me, free-ranging simply does not work. Every body has a different situation so you need to evaluate your goals and your area, and then come up with a plan that is best for you in your unique situation. And remember to have fun along the way!