So... what exactly is the "enemies level up as you do" system?

I don't know when it will happen, but I'd really like to play this game again soon. However, how exactly does the whole thing about enemies levelling up "as you do" work? Are you supposed to stay as low level as possible, so the enemies stay low level, otherwise you risk making them too powerful and make more work for yourself, or are you still supposed to make yourself powerful, but not grind too much?

I remember getting stuck on the boss at the missile base, because it kept attacking for 300HP, and I had 100-ish HP at the time, I think, because I was always too lazy to grind back then, (I would always cheat the level up, when needed), and I think I ended up winning by dumb luck. So, do I need to grind a little to get my HP up, at the very least, or is their a junction thing to raise HP that I should use?

You want to keep your levels low, because enemy levels scale with your party level, but more importantly, the party gets crap for stat upgrades when they level up as Junctioning is everything in this game for them. So "grinding" in this game is really more about drawing or refining spells to Junction onto your party. This is also why abusing GFs is a worthwhile strategy because enemies don't scale with them and if they get the "kill" they get all the XP instead of your party and the AP needed to teach them new skills.

So basically, the simply strategy of drawing all the spells you need in battle and then letting the GFs beat all of the enemies for you is ideal. Card Modding the enemies also allows you to defeat opponents without leveling up. This should allow you to get the spells needed to make your characters stronger while also keeping enemies weak. It's important to keep your Junctions updated though because enemies do have base levels, so even keeping your party below lv. 10 isn't going to change the fact some bosses have a base level of 30, so you'll need those stats cause even sturdy high level GFs can be beaten down pretty easily in the late game due to this and many of them sporting anti-GF spells.

Drawing can be pretty tedious, so you should focus on acquiring Refine skills from GFs which allows you to change all the useless items in your inventory into magic which is generally a much faster means of getting 100 of a spell than sitting there and drawing magic from enemies in encounters.

Another thing to note is that it is very easy to level up characters in this game, so technically, low level runs tend to be more difficult to accomplish. For the most part, if you keep your Junctions updated, the boost enemies get in levels isn't a big deal, it just gets annoying in the late game when bosses have close to a million HP and your stuck with the damage cap. Lv. 100 Ultimecia isn't really any more difficult than a Lv. 40 one but it does take forever.

Thank you for explaining, I especially appreciate you mentioning the GFs, because I wondered how I was supposed to have them learn things, but forgot to ask. Thanks.