Honestly, this is worthy of a far deeper discussion, but in brief:
Farming: Tiller, Artisan - if your goal is cash, there is no other viable option. Although if fields of ancient fruit is your plan, you can respect on the last day of Winter to Tiller/Agriculturalist, plant them on Deluxe Speed-Gro on Spring 1, then respec back on Spring 2. You spend 20,000g and earn far more back.
Mining: Miner/Prospector. Miner is mandatory for getting enough ores going to build the infrastructure. Remember, every keg is one copper and one iron ingot. So that's 30x iron and copper *per week* to match my oak tree stand's yields. That's 150 ore per week I need to collect. So Miner is a no-brainer. From there, I will be using every last ingot I craft, so increased sell prices are entirely useless, and Prospector (finally) got fixed so it actually does what it says it does. It still isn't much (a percentage chance on top of a percentage chance), but it's better than literally useless. Geodes and Gems are negligible.
Foraging: Depends on what I'm doing, really. Gatherer/Botanist generally speaking, but if I'm still looking for artifacts, Gatherer/Tracker has its uses, and it isn't expensive to swap back. New in 1.4 is the idea of going early Forester for more wood to build your infrastructure faster, now that it is actually useful. Lumberjack vs Tapper is a wash since both are fairly useless, but I suppose Lumberjack is marginally more useful in building infrastructure if you get it soon enough. So... early game, Lumberjack, then as I unlock the ability to respec, Gatherer/Tracker until I get the artifacts, then swap to Gatherer/Botanist.
Fishing: I despise the Fishing minigame, so I rarely bother getting enough levels to matter. Having said that, if I absolutely must, Fisher/Pirate can be useful in getting missing artifacts to Collect Them All(tm). Trapper/Luremaster is of minimal use, it's basically free Worm Bins. But I suppose it's better than Trapper/Mariner since the 'junk' is frequently much better than the shellfish I would normally get from the pot.
Combat: Crit-fishing is useless, so Fighter/Brute is the only mechanically sound option. Assuming one wishes to bother.