Here is a copy of my tips for reaching 200th floor:
1) I believe the first dungeon (The Cave) is the easiest, so it might be the best pick.
2) If you are also collecting loot make sure that you have at least two inventory panels.
3) Be prepared! Stock up on keys, potions, scrolls. They will help you greatly.
4) There are two types of shortcuts: dangerous passage (which allows you to skip 5 levels I believe) and second which requires you to have monkey eye gem. Use them as often as possible.
5) Collect monkey eye gems (see point 4). How to obtain them? They are in the boxes on the pedestal. How to open them? There are floor panels with minigames you need to solve in order to unlock them. The first one is 7 rounds of Simon Says, the second one is wires minigame (you need to drop all 3 stats to 0).
6) Take your time. After fight don't drink potions, if your position is safe just stand there and let your health and magic regenerate. It will be necessity in later levels when there will be almost constant onslaught of enemies.