Farming: Tiller/Artisan, because money. What Shneekey said, basically. Agriculturalist can be good for money late game if you hoard all your stuff and then swap to Artisan to sell them all at once. My issue with Shephard/Coopmaster is that you'll still be processing most animal products (to get cheese, mayo, wool, etc) so even if you're doing a lot of animals, Artisan will still be giving you a big profit boost. I guess if you have a ton of rabbits, Coopmaster might be good because iridium wool has a chance of giving multiple cloth?
Mining: Miner/Blacksmith, because I like Skull Caverns, iridium bars sell for lots of cash, and there's really not all that much you can craft with them so after a while there's really nothing better to do with iridium bars (at this point I'm getting 70ish bars per run). Even if Prospector gave me enough coal to craft all the bars (which it wouldn't), the extra 500g per bar from Blacksmith is still worth more to me that the 250g cost of buying coal from Clint.
If I wasn't doing SC, I'd probably go Miner/Prospector. An extra guaranteed ore per node is really nice when farming for ore, and Blacksmith is completely useless if you're not selling iridium. (IIRC it's either better or equal money to just sell raw ore instead of smelting it, if you're selling copper, iron, or gold.)
Excavator can be useful if you need more geodes to finish the mines (especially now that Sandy no longer sells infinite omni geodes).
Foraging: Gatherer/Botanist, because I like having all my forageables in one stack each, and iridium quality berries are nice Skull Caverns food. But honestly this whole skill tree isn't super important to my playstyle. Forester/Lumberjack might be nice for the extra wood, maybe I'll try that sometime. I guess Tracker would be nice if you really need more museum artifacts, but the one time I used it I found I wasted almost as much time trying to figure out where the arrows were pointing as I would have running all over the map. Maybe I'm just bad at using it. Tapper is pretty bad IMO, I can't imagine many people sell significant amounts of syrups.
Fishing: Fisher/Angler for the money I guess, maybe switching to Pirate late-game if I still need some artifacts that can be found that way. I've never done many crab pots, don't really enjoy the chore of collecting and re-baiting them every day.
Combat: Scout/Acrobat. There's this cool thing you can do with a hammer, where you do the special attack (right-click on PC) and then mash the regular attack (left-click or C on PC) and you get a bunch of strong area-of-effect hits. (And no, this isn't a glitch IMO, CA knows about it and deliberately hasn't taken it out, he referred to it as "the club quirk" in update 1.4.1 and specifically removed some animation bugs caused by doing it.) So if you get Acrobat, and then enchant the hammer with Artist, you can do this almost once a second and it makes fighting a lot easier. I agree that Scout is pretty awful, though. The improvement to the dagger's special attack means they're actually decent now, but IDK if any of the "high crit chance" daggers are actually good enough to fight strong enemies with.
If I wasn't doing the hammer thing for some reason, I'd probably go with Fighter/Brute for the reasons Shneekey said.
