What carries over to NG+

Everything carries over, even Special Items tied to missions, so don't do it till next patch.

As far as I can tell everything that is important, but the things you find in the game (not purchase) will disappear, such as the model ships you find on remote planets.

There is one thing to know about a NG+ game you will have the drone unlocked still but if you go to respec you will lose access to it until you complete the requirements to unlock it again so if you want to respec I would suggest doing it prior to starting a NG+. The other quirk is you will keep access to your extra consumable slots from AVP even if you don't buy them again.

Edit:

In NG+ there is also one bugged quest.  If you upgraded the shields on the Nomad you will still get the quest to upgrade them via crafting, but since those upgrades continue into NG+ its impossible to complete.

I found that the consumables didn't give me all 4 slots back in NG+. They were technically there when I pulled up the wheel, but you could not actually activate any consumables filling the next 2 slots so, so the AVP bonuses had to be unlocked again. 

I like that bit about the color as well, but just a tip if you're hung up on tiny details like I am, I would reset the armor back to the default color before the final save. The Initiative helmet you start with in the game will reset back to its default color when Alec Ryder reaches the remnant controls on Habitat 7 just before the accident. My armor was basically all black at the start of the game, but then the helmet turned white. That alway bugged the hell out of me.

That's true. Since it lasts for only a brief time, I don't make any effort to change the color of my armor before starting my new game plus

Yep, it will be better to wait for a patch if you are planning to do NG+.
I played only 3 hours on NG+ and I find a lot of odd stuff.

You will definitely have problems with some missions, movie night for example; I didn't wanna risk to trigger any other bugs so I just reload my save before my 2-nd conversation with Lexi /she already start to talk about movie night before I even get that from Liam/ and I will wait for a patch.

The Movie Night bugs are just bizarre.

If you talk to the mods merchant on Kadara, you immediately get 'The Final Piece' part of the quest chain without even needing to talk to Liam about movie night in the first place :/

Right now I'm just hoping that by not actually completing the quests out of order, it'll still trigger everything properly.

Got a bug where one of my crafted weapons didn't carry over, so don't have Vintage Heat Sink & Seeking Plasma Rounds augments unless I'm blessed by RNGesus and find it in a loot box or off a dead enemy

Based game weapon, crafted Cyclone AR with vintage heat sink and seeking plasma. Did ridiculous damage, loved that weapon and now it gone. Hoping I'm lucky enough to find the seeking plasma augmentation. Getting some really good results off my new crafted Soned Assault Rifle (Kett minigun)

My OCD would've demanded it. No judgement here.

I haven't experienced any bugs with Suvi and Vetra. Their dialogue to actually ask for the items triggered on schedule for me. I think the bug does allow me to just interact again to submit the items without having to purchase though. 

I had a persisting issue with Lexi where Ryder was handing her the liquor, and now that I've avoided "unscheduled" dialogue for a period of time, it no longer occurs and I can talk to her normally again. Hopefully, her dialogue will be correct after Journey to Meridian. Jaal's persists though. I suspect if I avoid speaking with him outside of aftermath dialogue, his request dialogue may trigger like Suvi and Vetra's when the mission his dialogue follows is complete, or at least that's the hope. Man, maintaining proper order of Movie Night is like a job or something lol.