Your fireballs create space and give you opportunities to poke/grab. Otherwise, as far as strictly spacing goes you have 2 main options.
1: Ftilt. This is especially useful after whiffing a move when your opponent rushes in to punish, and is the longest-ranged move we have on the round. No real followups after this, unfortunately.
2: Bair - A perfectly spaced retreating bair can't be shieldgrabbed, but can still be punished in other ways. In an aerial spacing war, however, this will be tough to beat.
As far as the neutral goes, it's more about creating opportunities to get inside rather than poking and footsies, but they do indeed have a time and a place.