Special professions are straightforward.
Construction = building buildings and making tax certificates for your property. This isn’t something you want to power level, but do upgrade this proficiency as necessary. That way you’ll have more labor available to use elsewhere and make money with.
Larceny is opening drops (coin purses, crates, etc.) from mobs. This is very important for leveling up Hiram gear, as you’ll burn through a TON of labor obtaining synthesis materials to upgrade your gear. You’ll want to level this up as much as possible, too.
Commerce is still a very profitable system. If you do it correctly, you can make more silver/labor than virtually anything else in the game. However, staging trade packs (crafting packs in bulk and letting them sit on your property until you’re ready to move them) isn’t necessarily the best idea, as it will cut into your profits. The value you get from staging depends on which packs you make and where you’re turning them in. A direct implication of the changes to the trade system is that coastal property is no longer the absolute best location. Pick whatever land is best suited to the crops you want to grow and whatever else you plan to use it for.
Artistry is a purely fun proficiency. It allows you to make sheet music to play with your instrument. The higher your proficiency, the more accurately you play your songs and you can play longer songs.
Exploration is an end-game thing. You could theoretically use this as a money maker by crafting copper/silver/gold keys (which open certain crates from mobs) and selling them. It’s main function is to unearth sunken merchant ships and to obtain packs based on your exploration level. This is a very time-consuming, risky activity that requires a merchant ship and a submarine, which are expensive gilda star items.