Tetra's ship is my hands down favorite counterpick. The water is perfect for his spike(shed dairs out of water are perfectly timing to hit almost any character with ease, and his dairs in water kill at extremely low %s, something only a couple characters can say besides him.) And in addition the water acts as a buffer to his recovery, though you have to be more careful not to PKT directly into the side of the ship on the left side if you don't wanna die. In addition, the falling ship after the tornado makes it much easier for Ness to get below someone and tailwhip somebody into a followup PKT2.
Delphino Plaza also works, especially against floaty characters like Dedede or Kirby who sometimes like to float just below the bottom floor...can you say spike? Cuz I can, and do, often. The water parts are extremely useful with Ness's spike, just like Tetra's ship, but less avoidable due to the high walls surrounding it. There are also many parts in this level with a walk off level, and Ness's forward air is extremely good at these parts, but don't EVER try this against a Dedede, just avoid geting in front of him on those parts and play it VERY safe.
As for moves, ideally his PKT2 will be his best game evening tool, with its new way of working, it'll be a good way to get low % kills and rack up damage.
Fair is a great move to keep almost anyone away, and it's one of the best pressure moves in the game now, with L-canceling gone. And with reverse aerials(dashing, and then pressing in the opposite direction you're running at the same time that you jump facing the opposite direction you were running) you can mix it up between fairs and bairs with relative ease to work mindgames into your aerial game. Ness's rising aerials also make for mindgames with relative safety.
PK Fire goes a little farther now, and definitely hurts people a lot more(in terms of overall damage and holding power) so it'll be a good move against ranged people, though I don't suggest using this move too often against Meta Knight, as his ability to punish lag is not worth what this move does.
PSI Flash has uses which I have yet to fully explore, more on it later. It won't be a good move for your purposes though.
That's about all I've seen so far.