You should generally target Nana first, since even though wobbling is pretty much off the table while you have both Climbers, killing Nana cuts the other person's power in half. Desyncs are good, though using them predictably will probably get you hit by a wavedash into smash attack. Back-throw into wavedash down smash or forward smash is really good because down throw won't do a good job separating the other Climbers. If I notice the other person abusing wavedash into smash attack, I like to go for short-hop or full-hop forward airs depending on the smash attack I think they'll use, although the timing is pretty strict since down smash and forward smash both have good hitboxes. Using tilts and jabs should not be underestimated, especially when you're not sure if you can commit to a laggier move (like a smash attack or an aerial) since you can throw out an f-tilt or a jab and then react appropriately. I would recommend using back airs sparingly because they're strong but do not beat smash attacks in most situations. Covering recoveries is pretty straightforward, you should respect the up B hitbox and hit them off stage again when they're in landing lag. Side B is easy to react to as well. The key to winning neutral, in my opinion, is mixing up your movement and approaches. If your opponent knows that every time you wavedash in you're going to try to down smash, they shouldn't have a particularly hard time beating you. Change up the lengths of your wavedashes, incorporate wavelanding, use shieldstopping, dash attack, etc. so the opponent has a harder time figuring out what you're going to do and when you're going to do it.
Hope this helps. I'm by no means an expert in the matchup, but I have some experience in it and these are all concepts I've found to be important.