Full jumping is legit. If they follow you to punish you before the peak of your jump, you can airdodge and cancel the ending lag to make it lagless. If they don't then you have a number of options. One of the best and most under used options when it comes to approaching is fast fall empty jumps. Also rolling after a jump since rolling is legit in this game. You can use the empty fast fall full jump to cross them up and roll to the the other side again to cross them up. Also if they come up at you, you can easily jump away.
On the ground walking is incredibly op and should be abused more. If youre just rolling around, or running everywhere, take a break. Your circle pad will thank you for it. When the time comes for you to go in, you have an incredible amount of options from standing/walking that covers a great amount of distance quickly. His best range has always been mid range. Keeping them in reach while staying out of theirs.
Dash attack: This move will be a great and go to option because of it's lingering hitbox. It lasts a long time and can even catch rolls at the end of their invincibility.
Boost Pivot Grab: This move covers an amount of distance that is greater than any roll relatively quickly.
Pivot F-tilt: If you dash up to them and theyre still shielding, a pivot f-tilt at the back of their shield while you slide away. Its a great move, and it feels like it has as much lag as a whiffed first jab.
Cross up Roll: Because rolls are OP, they should be used, and abused. Cross up roll is great because it gets into them, AND behind them. Especially if they're shielding, then their options are even further limited. Also this lets Fox get in where CQC is incredibly dangerous.
Walking: Just walking up to them and staying right out of range of their fastest poke is also a great option to see how they react. If they throw out a normal and whiff, laugh at them and punish them with Fox's great closing tools. If they throw out a projectile to try and get you out of their space, reflector, and cross up roll, or sh nair/dair or whatever aerial you please. Again, Fox's best range is mid-range.
Silly ground approaches that shouldnt be used but will be posted anyways.
JC Illusion: This is the baller approach despite being incredibly dangerous, and easy to read/interrupt. The end has practically no lag, and people with no Fox experience will not know how to handle Fox just zipping back and forth on the stage making him practically uncatchable.
Firefox: THE TRUE BALLER APPROACH! If used on the ground and angled correctly it has no lag. Also people wont know what you're doing and will be absolutely confused thinking they can just shield it and that it has a lot of lag at the end. Spoilers, it has none.