Dair can be pretty good. It's got low landing lag. You mentioned shields, and if you're able to dair on top of them and just behind them, it can pressure their shield without the fear of getting grabbed. With the low landing lag, it can make it more difficult to punish with an aerial out of shield as say n-airing behind a shield. If the dair hits, it's often a free grab.
Nair can be good, cuz it's a constant hitbox. It'd beat out a falco phantasm, pika quick attack, etc.
Umm, Mario has a pretty good jab if you need it after landing a nair or land near an opponent.
Don't forget about basic options like shielding, walking, grabbing, etc. If they keep hitting you out of approaches, shield. If they're shielding, grab. If spacing is the issue, work on that and think of the spacing of each of your aerials, (short hopped vs full hopped, tilts, grabs, etc.
