Any suggestions how I make a 'rich' character?
A Farmer maybe?
Oh and I'm always out of platinum coins since I tend to get every crafting and collecting skill.
Could you tell me which are 'must-haves' and which are useless?
If you have the patience to raise performing, the party jobs can pay very well. It isn't unusual to get 10-15k from a single job (or even from a single performance). Granted, it requires around 25+ performing to get anywhere. If you can get a ranch, use it to raise a bunch of low level monster and practice performing there.
Another good way to make money is by doing random dungeons. However, to be truly effective, you need to complete the pyramid invitation quest to get the statue of opartos (which allow you to reset every completed random dungeons).
Something I never tried myself, but might be effective is by gathering tons of engagement ring/amulet in puppy cave and marrying some of your companion. You get some gift everytime, including a potion of corruption (everytime I think, but I am not sure). For further profit$, you can bring the companion to port Kapul to do the wife collector quest (at the cost of some karma).
As for crafting/gathering skills, I usually only get anatomy, cooking, farming, mining and, if I chose Ehekatl of Luck as god, fishing. Of these, I only consider cooking and farming as "must-haves". Anatomy is great, but you still get plenty of corpse from your ranch without it. Mining is mostly good when doing dungeon crawling because some floors require you to dig your way between rooms (or teleport, but that's unreliable). Fishing is worthless unless you follow Ehekatl and even then, not really needed as corpses can do the job of raising favor well enough.