For maximum efficiency you'll want to focus on the watering can first since it's used constantly and the upgrade timing is critical - wait for the weather forecast to show rain then immediately take it to clint for the copper upgrade. The pickaxe should definitely be next, crucial timing here since you need that steel upgrade to handle the tougher ore nodes especially past floor 80 in the mines. Getting your axe to steel is the next priority specifically because it lets you access those large logs blocking the secret woods, which opens up hardwood collection.

The hoe can honestly wait until you've got a decent sprinkler setup going, since early on you won't be tilling massive field sections anyway. One interesting detail about the trash can that often gets overlooked - upgrading it gradually increases the refund percentage you get when selling items through it, maxing at 60% at iridium level which becomes super valuable during long mining runs.

Timing-wise, remember all upgrades take two full days to complete so plan carefully around your watering schedule (you get your upgraded tool at the third day). For mining-focused playthroughs, you might actually want to prioritize the pickaxe first, but the standard order works best for most situations. The final iridium upgrades require some special volcano materials later on, but that's way down the line once you've got the basics sorted.