The main thing about Splatoon's SP is that it's a tutorial for onlineplay that was hampered by the ability to use only a single weapon. Having majority of weapon types available in the sequel, having more nuanced platforming options and enemies can definitely prepare you to a certain degree for TurfWar and Ranked.
Personally I had the girl amiibo and played the final boss with a charger a bit before trying to master the weapon and I believe it helped. So I'd recommend new players to experiment in the SP before jumping into the online matches, the most important thing in Splatoon is finding the weapon that compliments your playstyle. Buckets, Gals, Chargers, Shooters, Duallies, Rollers, Brushes, Splatling and Blasters all provide a great variety of play options. Each weapon has a varied requirement in terms of map awareness, aim, platforming/movement, zoning, coverage etc so the campaign this time will be able to prepare new players much better for the online matchmaking.
There is also specials and sub abilities to learn and eventually you can get into the gear perks but those aren't really important in the beginning since it will take a while to build up a wardrobe