So far I have found mechanics and stealth to be the primary useful skills, followed by athletics for certain scripted encounters to avoid injuries, but it's not strictly necessary.
With mechanics, you can disarm traps to reach difficult areas, open chests and get things like sapphires and unique weapons, pick important locks, etc. One perfect early example is the vault in Queens Berth.
You may want to get a second character with a lesser amount of mechanics and an adequate amount of stealth so that you can squeak past guards and steal items from vendors. For example, with a spark cracker, you can grab patinated plate, worth 30k from the merchant from a crate sitting right next to him. But you don't need as much stealth as you do mechanics. I would aim for at least 15 group mechanics on your primary lockpick by level 9. You can usually walk up and pick locks with them in broad daylight and then steal it with your stealth character afterwards. There is treasure sitting right in the middle of every city and you can take it under their noses.
I don't even know what the other shit does, nor do I care. I like having athletics as a point dump for a free backup heal. On rare occasion, alchemy has shown up and the threshold for skill checks is usually enough low anyway that the base for certain classes is enough.
As far as conversation checks, I've picked a favorite persuasion for each character to pump one, and my PC usually has enough with that to pass the skill checks I've encountered so far. I imagine at some point 7 or 9 skill level isn't sufficient, but oh well. The checks rarely do anything important anyway.