I really envy you your sweeping backyard. If it were me, I'd focus on some natural planting along the back that I could view from the deck. I'd muck around by the creek, cut down the tree of heavan (ailanthus) and plant red maple, pin oak, sycamore, basswood, hemlock, river birch, sweetgum, nyssa sylvatica (common name escapes me, maybe black gum?) and silver maple. Some lovely specimen trees to look at, many with interesting winter bark. Then I'd plant some understory flowering shrubs--native rhodies (the carolinia ones, can't remember exactly, they smell great), witch hazel, amelanchier, sweetbay magnolia, spicebush, viburnums, etc. Then underplant with some pretty spring bulbs. I'd be vigilant to keep the poison ivy at bay. wood chip it, etc. Then sit back on my porch with some lemonade and watch the birds at the feeder. Up by the deck I'd plant some persian lilacs for the heavanly fragrance. A little grove of japanese maples and japanese white pine because I think those trees are gorgeous to look at. Then a big apple tree. Someday I might put a brick patio at the bottom of the deck, with a pergola over it, with a climbing rose and wild clematis providing shade. My cousin has a similar back deck with a pergola, and the wild clematis does a good job of cascading over it. My reasoning for doing decorative trees and shrubs and a more natural landscape is once they get started, much less time spent fussing with them than perrenials.

Transplanting of mature producing plants usually doesn't work. But what would you loose?) Only thing is, I wouldn't put them in the pots. I would use burlap, or even plastic sheet. Dig the plant out with as much soil as possible,place on the sheet and wrap. Then move and try planting without much disturbing root ball. No pot will hold roots grown in the bed.

https://www.bhg.com/gardening/pests/animal/the-top-deer-resistant-plants-for-your-region/

Photo 1 has daffodils. When the foliage dies back you can remove it. Photo 2 is pachysandra, an evergreen groundcover that can be a bit boring, but is good to leave unless you have something else you want there. Photo 3 is a peony Photo 4 has Rumex, a tap-rooted weed on the right. Use a dandelion skewer to remove it. On the left looks like it might be the self-seeding biennial Lychnis coronaria. For future IDs, the Name that Plant forum might be a more appropriate place to ask. There are some real whizbang plant experts there.