You should deal damage whenever healing is unnecessary. Naturally, it's okay to start off skittish and unsure when healing is and is not necessary, and if you dedicate yourself to it I'm sure you'll be able to get used to when it is and isn't. Of course, try not to be so skittish that you never deal damage - the best way to get used to when you should and should not is by taking risks and trying it.

Worst case? You wipe, say "Sorry, pushing my limits a bit, I'll reel it back in there!" and move on.

As for when to use Cure I vs Cure II, you use Cure I when your MP is stretched so thin that you cannot afford to use Cure II, as its MP:Healing ratio is better and it has the chance to proc a free Cure II.

However, since Cure I's healing-per-cast is so much weaker, you generally want to avoid using it (Freecure is generally a trap) wherever you can, and instead use Cure II, Afflatus Solace (an equivalent to Cure II that costs a Lily instead of MP and has no cast time), Tetragrammaton (an equivalent to Cure II that has no cost but can be used only once every minute) and so on. This is because to heal the same as (technically slightly more than) a Cure II you need to cast Cure I twice, meaning if you instead cast Cure II you could have cast Holy, Stone, Aero, and so on as well, provided your MP can sustain this (it usually can).

As you level you will get more and more tools that both reduce the number of times you need to cast Cure II (sparing you from spending MP on it) and increase your MP efficiency (meaning spending MP on it is less draining on your overall reserves). This means that generally over time Cure I will see less and less use, unless you hop into super-hardcore Ultimate raiding or similar, where I hear the world-first players resorted to using Cure I to spare their MP... But if you're taking on the toughest content in the game, then you're probably experienced with and good enough at your class that you don't need my advice any more!