For that size building I would recommend you spray foam it yourself. I put a lean to off the end of my shop a while back then ended up closing it in a few years later. It’s roughly 24x14 and I bought the touch n seal foam kit. I think it was the 700sf pack. Did it myself in a couple hours and turned out great.
I will look into to that. Didn't know something do it yourself was available. Thanks.
To address some of the other concerns here was some of my thought process and info I left out.
The only reason I was considering between 2x4 and 2 x6 was the price. Yes the price between 2x4 and 2x6 is small when standing at the lumber yard. But when I'm standing in my barn looking at the over 100 8' 2x4s I have that I salvaged from work as scrap that was built into cribbing inside train cars and got for free the price between the 2 goes up quite a bit. But they are 8' not studs and would all have to be cut down If I wanted 8' walls not 8'3" and the added insulation should save money in the long run so I was kicking around the instant savings vs time and long term savings. I could just make the part that would be a cooler have double thick walls and insulation when that comes into play after all.
Honestly I was considering just buying a yard barn to be faster and retrofitting it but besides that being more work I wanted to build one with the boys so they get the experience. But after how they talked and acted to and with their mom yesterday. The boys are not a concern and I should have a lot more time in October and November considering I could care less about spending my time taking them hunting this year. So I still may just buy one and spent the time saved doing something else. I have not has an available Oct or November in over a decade and all my vacation time to use then.