I'm on my second run, after taking a save to autumn and deciding to start fresh with what I'd learned. Copper to me is a pretty high priority just to get a saw and start making planks - it's more a huge QoL upgrade than a necessity for survival. Panning sand is much faster and more reliable than picking up rocks, and both games I got copper spearheads while panning, too. My priorities are:
Bags
Storage pot
Cookware
Fenced crops
Cellar
Pan for 40 copper
Mine 1000 copper for anvil and saw
So, I'm panning for copper by probably day 5 or 6, and it will take 1.5-3 days, getting other minerals and gear, too. This second run, I had my cookware on the first night and my cellar on day two, so food was never an issue, but there was some lucky RNG in the mix.