I try to upgrade my pickaxe as soon as I can, axe comes after. For the fishing rod I rush the fiberglass rod cuz I hate waiting for fish to bite, and if I buy the iridium rod really depends on if I want to go for legendaries now or later (on my current save I want yo try to catch them with challenge bait so I'm holding off)
I always forget about upgrading hoe and watering can, maybe upgrading them much later than everything else just so they don't stand out, being stone in the iridium tool set.
Trash can? Yeah I'm not upgrading that until I randomly remember you can do that in year 3 or something lol
I really rush the first backpack upgrade because I hate how little space we're given at the start. And I buy the second one when I have the money for it that I don't need for anything else