i love jrpg stories but i hate grinding (enough to not finish ffvii).  do i have to grind much to play this game.  Also will i have a problem with miss-able stuff?

grind for draws, and card enemies instead of killing them

You can beat the final boss at lvl 15. VIII's now infamous "everyone levels with you" system makes it possible.
 
However, as was already mentioned, the game also discourages just rushing through the game, as vital stuff is easy to miss, and not farming enemies for spells regularly makes it decisively more difficult.

You should take the time to draw magic, but don't spend too much time focused on grinding your levels.  The key way to boost your stats is through effective use of the Junction system. As Eirikr said, the enemies in the game level with you, and so if you get int the later game boss fights with a high-level Squall, you're not doing yourself any favors.

"You can beat the final boss at lvl 15. VIII's now infamous "everyone levels with you" system makes it possible.  However, as was already mentioned, the game also discourages just rushing through the game, as vital stuff is easy to miss, and not farming enemies for spells regularly makes it decisively more difficult. "

" @Meowayne said:

"You can beat the final boss at lvl 15. VIII's now infamous "everyone levels with you" system makes it possible.  However, as was already mentioned, the game also discourages just rushing through the game, as vital stuff is easy to miss, and not farming enemies for spells regularly makes it decisively more difficult. "

Wait what? i don't remember this "everyone levels with you" system, unless my memory is wrong, which it could be, it's been a while, characters only levelled if you usd them in battle, like always.  End of disc 3 is really where most people will have trouble i'd say, apart from that, i don't remember a lot of grinding. "

Try to level up as little as possible, instead choose to draw the shit out of monsters, since equipping spells to your stats is much more important in the long run.
 
As people have said, monsters scale in level to Squall (or your highest lever character i think), but if you stay low level but have some good stuff equipped to your stats, you´re basically invincible.

Also, something to remember is that summons are pretty useless in comparison to spamming limit breaks (which is easy to do). I do remember a playthrough where I didn't use a single one except for Doomtrain, and that's only because he causes status ailments. 
 
The sad, simple secret for success in FFVIII is to use the Aura spell (or get your HP down to 1/4), then jam on the turn skip button until you hear the limit break chime.

As Eirikr posted, you don't have to grind because enemies usually share the same level with you however there are some quests to follow. I played the game 4 times and finished almost every quest avalable except the card quest and the chocobo quest. What's good about this game is that it breaks the mold of traditional JRPGs, you are grinding just by following the story. After having played it so many times I discovered that in order to avoid missing summons [the most important grindable elements of the game], you must use the draw command on every enemy on the playfield, above all try to draw unknown magic "???", some bosses have GFs hidden as ??? magic like Elvorett in the comunications tower in Dollet, I had to replay the game to get Siren from this boss so I learnt this lesson in the hard way; the same will happen with Brothers, Carbuncle and Cerberus as far as I can recall
 
You should read a guide or faq on getting the GFs because even though there are very few quests in the game, the ones that matter are a pain to complete [particularly getting Doom train or Eden but not so much]

" @Eirikr: I dunno, remember getting reaaaaaaaaaaaally stuck about 2/3 of the way in and Could not go any further because I had missed unobtainable Summons  and ended up having to use a friends  action replay disk because I didn't have the means to progress past a 3 headed dog boss. "