There is already this question clarifying that you cannot cast spells with a range of self on the Shield Guardian, as you need to be able to target the guardian with the spell. It is clear that you can cast a spell that targets a creature "on" the guardian, as the guardian is a creature.
But what can then be the target of that spell, when the Guardian activates it? The description of the Spell Storing ability says:
the wearer must cast the spell on the guardian. The spell has no effect but is stored within the guardian. When commanded to do so by the wearer or when a situation arises that was predefined by the spellcaster, the guardian casts the stored spell with any parameters set by the original caster
I would take the target to be one of those parameters of the spell, and I am forced to target the Shield Guardian with the spell to be able to store it. Does that mean that it can only store spells targeting a creature, and those spells then effectively will have to target only the guardian when released? Or can there be a second, different target set for the spell when storing it?
This Q&A (which is confusingly titled to not ask anything about the spells storing aspects) indicates that any parameters not set by the caster can be chosen freely by the Shield Guardian, but is the target one of them? This Q&A states they plan to store Greater Invisibility into the guardian "with the intent to cast it on the party rogue", which would imply you can set another creature as the target, but the answer does not address this, either.
The second part of the question is: can you store a spell that targets a point in space? If the caster selects a point in space "on" the guardian, for example as the target of Fireball, could they cast Fireball into the Shield Guardian? And if so, the same question as above, can they set a separate point in space for when the spell is released or leave that up to the guardian, or will the Fireball have to be centered on the Shield Guardian?
Lastly, as a very specific case, if you can select a point in space, and can set (or omit) new targets, can you store Dimension Door into the guardian? The spell has a range of 500 feet (targeting a point in space), not Self, but it says "You teleport yourself (…)". Would it then teleport the guardian, who could possibly elect to take one other creature with it? (This would be pretty sweet, as my caster cannot Dimension Door himself and take the guardian along, as the guardian is large).
Best Answer
You will need to work this out with your GM
You've noted the two salient points:
RAW you can say that "cast the spell on" means you can't use a spell with the range of self, but there are multiple examples in the rules of spells being used "off book"; for instance, the Intellect Devourer can be driven out by casting protection from evil and good on it, but that spell can only be cast on a willing creature.
The term "parameters" is equally or even more ambiguous. "Parameters" isn't a game term, and in particular it is not clear to what extent the "parameters" must be decided at initial-casting versus actual-casting. To my reading, a "parameter" could be "the creature I point at".
In the end the GM is going to have to interpret what these things mean in the context of your game.
A good way to handle this is to come up with a way that you think will work at your table and suggest it to the GM.
If you want your guardian to cast fireball or dimension door, then suggest it to your GM. The rules are flexible enough that neither of those is obviously contradicting the rules, so if it works for your table, go for it.
The SG description says:
I think this theme is at least as important as the exact wording. I don't think it means the guardian can only use its magic when the amulet wearer is rendered helpless, but the idea of the guardian doing something unexpected when the chips are down is a really fun one.
What has worked for us
We were faced with the same issue when my wizard finally finally found the guardian belonging to the amulet.
My wizard's guardian has stored and used fly twice now. It's worked out really well. In one case the wizard got knocked down to zero and the guardian activated fly, grabbed the wizard, flew off 50 feet, and stood guarding the unconscious body until help arrived.
We play the guardian as a not-very-smart automaton who understands ideas of protection and safety very well. Examining the battlefield and getting the wearer to safety? Got it. Complex instructions involving lots of angles and math? Not so much.
What we've found doesn't work is when my wizard's shenanigans bog down the game. Sure it's "teleport us here" and "teleport us there", but when you want to get fiddly with the shield guardian suddenly they're bored. Ingrates. So anything I want the guardian to do (like fly) I work out with the GM out of session so that it can be executed quickly in session, and keep the focus on the players and the action.
Good luck!