If the PQI challenge you've been assigned is manageable, it's usually your best choice. However, PQI gets progressively more difficult the higher your completion percentage, so always do a sanity check and ask yourself "is the reward worth the trouble?" because at a certain point the answer will be "no". (my PQI is permanently fixated on vicious dungeons due to my high completion %; it's a pure money-loser at this point).
The flaming dungeons are usually a safer bet. Use the "bet on the boss" preparation if you want to further increase the value of the trophy. This is less than what you'd get from the PQI, but it lacks the class/race/badge restrictions so it's easier to clear. Another good approach is to aim for 100% completion. You get additional cash for new badges and class completion (and a pretty big payout for 50% and 100% completion on a specific dungeon) and that can add up.
Finally, when choosing preparations try to pick low cost ones. "Extra attack boosters" is a great one; it costs almost nothing but on a 10th level character it adds up to an extra 10 points of damage. The altar preps (except for "extra altar", which is pricey) are all very cost-effective choices, and a good altar selection can make a dungeon trivial. Jehora Jeheyu, Glowing Guardian, Binlor, Earthmother, Taurog, and Mystera are all particularly potent choices with the right combo backing it up.