According to the description of the time stop spell, it ends if I affect another creature or their stuff. But suppose that I cast time stop, and during my next turn, I attack an opponent or cast a spell at them.
Would I get advantage on the attack or spell? (And if so, would a spell that has a saving throw impose disadvantage instead?)
I figure I would, because it's very easy for me to hit the target if time is stopped for them.
The answer to this question highly depends on how the DM interprets the description of the Time Stop spell, more specifically the conditions for the spell to end :
This spell ends if one of the actions you use during this period, or any effects that you create during this period, affects a creature other than you or an object being worn or carried by someone other than you.
From this description, I can see two main paths for a DM to take:
1. The target is "affected" once the action is officially declared.
Under this interpretation, the target is affected as soon as it's being used in the mechanical resolution of an action. In this case, the target would resume motion as soon as your swing would start, and would thus be able to defend itself properly, which in turn implies that you get no special benefits for attacking someone during a Time Stop.
However, If you're going to use Time Stop to land an attack (presumably a powerful touch or ranged attack spell), the effect will end after your first shot anyways. In this case, since you get at least 2 rounds of Time Stop (1d4+1), I would use my first round to use the Hide action. Normally, only a halfling could use this action to hide behind a medium sized creature in the middle of a battlefield, but I would be inclined to rule that a wizard using Time Stop can quite easily position himself in the target's blind spot for one attack, since he is essentially moving faster than his target's eyes can perceive him. Time Stop being a 9th level spell, I would even grant you advantage on that Hide roll; 9th level spells are supposed to be powerful, after all. Once you are hidden, you would indeed get advantage on your attack roll by getting the benefits of the "unseen attacker" rules.
2. The target is "affected" once it receives the effects of your action.
This interpretation favors the caster of Time Stop much more than the previous one. In this case, the target would only resume motion once the attack or spell actually hits. It can't move, it can't defend itself, and it certainly can't talk while being time stopped.
This means that, for all intents and purposes, your target is "paralyzed" for the duration of your attack, a condition that makes it fail any STR or DEX saving throws. Furthermore, all attacks on this target would receive the benefits of advantage, as well as automatically being critical hits if you are within 5 feet of it (this is when you want to use that powerful touch spell!). If, somehow, you had access to multiple attacks during the Time Stop (like from the Haste spell, or perhaps a 2 level dip in the fighter class), the effect would normally end after the first attack, provided it hits. Whether or not the second attack would still benefit from advantage would be up to the DM.
Some DMs might argue that a missed attack also ends the Time Stop. I'd be personally inclined to disagree with this interpretation, as the target has not been "affected" if it receives no effect whatsoever, but it makes some sense if you consider that, mechanically, it was the target of an action which has now been fully resolved. If that's your DM's ruling, you should still receive the bonuses from the paralyzed condition... Just don't miss!
Spells do exactly what they say and nothing more, anything beyond that is left up to the DM to decide.
Time Stop doesn't say it gives you advantage or other creatures disadvantage, therefore the spell doesn't inherently grant these things.
However, a DM is free to decide what actions or circumstances do grant dis/advantage and a cooperative DM may grant such things if they think the circumstances would call for it and/or if you can come up with a strong enough reason as to why you think such things should be granted.
Also, the Advantage and Disadvantage section of the PHB says this (emphasis mine):
You usually gain advantage or disadvantage through the use of special abilities, actions, or spells. [...] The DM can also decide that circumstances influence a roll in one direction or the other and grant advantage or impose disadvantage as a result.
