I agree, I made the mistake of trying to build my first coop with 1x2s. They're always wiggly, and couldn't hold anything much bigger than a mad rooster. 2x2s or 2x4s are your friend.
I haven't ever been a fan of going to any store because it can be such an ordeal. First it's hard to find a lumber cart (and when asking where I could find one at Lowe's one day they told me to go to the backside of the parking lot and look!). Then there's the hunting through everything to find good wood. And then I nearly impale people trying to push the filled cart.
My last trip to Home Depot changed that. I had never had such good service that I have called the manager to thank the assistant before leaving the parking lot! He asked if he could help so I explained I needed some lumber, he went out and got me a cart, picked out the best pieces for me, loaded it, took the cart to the register and then waited for me to pull around and loaded it. It was nothing like the previous exasperating sweat inducing episodes i've had in the past. And none of the 'you're a woman so therefore know nothing about hardware' attitude.
I gave up on Lowe's after they sold me a junior hacksaw to build a chicken coop. My husband thought it was highly entertaining, I built that sucker with the hacksaw and it just about killed me.