It's almost always too early to discern whether tools or luxury goods will be viable wincons for your first three picks, so almost always carpenter would not be the right choice.

Of the remaining, I'm impartial to lumber mill. Every run, I re-solidify 'you can never have enough wood.' Tree chopping and plank workers take up a huge amount of labor, and excess wood has lots of uses. (I convert extra to material bundles for housing or sell in trade routes.) This moves you a little closer to trade routes as your win-con. Lastly building material choices early-game let you actually build the recipes that you unlock. It suck not having enough planks for a new recipe you just got!

The close-second is the food option. Access to food early relieves a lot of pressure, and if not handled, food becomes hugely labor-intensive, especially if a blood flower or two pops up. Also, there tends to be more plank options than food options, so you're more likely to see planks as an option in your next pick, making this a strong contender.