I never ever close my pop door, so my chickens can go from run to coop and back anytime they want to. I'm too lazy to get up at 0'dark-stupid and let the out for the day, and our schedule is such that I'd have times I wouldn't be around to put them back in anyway. Don't trust auto-doors for no particular reason other than I don't trust them, although people use them with great success. With my husband's position in his fraternity, we often leave town for days at a time and from the time she was 8 years old, our granddaughter has been in total charge of everything from the feeding to the egg gathering. She does an amazing job, and she's now 10 years old. So I need to have my setup as fuss-free as possible.
Our run is as predator-proof as possible, with a 2 foot hardware cloth skirt and hardware cloth apron. It's fully covered with chicken wire wired in over cattle panels to deter overhead predators and pests, and that hardware cloth protection extends all the way around the coop. In summer there is a sunshade covering the run, and in winter we use a mesh reinforced clear plastic greenhouse type cover. There are double latches on the doors. Only once did I have a "predator" try to get in, and that was our English Setter Molly. She got overexcited when the young chicks were turned out into the run for the first time and tried digging underneath to get them. She broke and bloodied a toenail and never tried it again - in fact she blamed the chickens for her "owie" and from that day on gave them wide berth, even when they were out free ranging.
I like my chickens to be able to decide for themselves whether they want to be in the coop or in the run. I don't have to try to herd them back in if the weather goes sour, don't have to teach them how to go in and out because the newer chicks just follow the older birds at night, and with our long winters here they don't have to be crammed into the coop until I can let them out. If one chicken is being picked on a bit, she has plenty of hiding places provided and can get there on her own.
What you do is entirely up to you. You'll find what works best for you as you go along! Just remember that predators don't always come at night - if they're hungry and they know there's a chicken dinner close by, they don't care what time it is!! Stray dogs can be a huge problem, so don't just think "wild animals".
Welcome to BYC!! Glad to have you here!