I've done a partial play through with new game + choosing the eagle path.  Which path you choose only matters at the start. You get 3 game + specific skills, an outfit and a weapon, for choosing a specific path. You can get the "other" 6 skills, although it costs 24 skill points. You can buy the other weapons and outfits once you reach the merchant at Kuwaq Yaku. Lara starts off with all of her inventory (like lock pick, rope ascender, ...), outfits, skills, and all weapons once a certain type of weapon in enabled. At Cozumel, if Lara had the lockpick from the prior run, she has it on new game + and can open the chest for 100% complete on Cozumel on the first run through. The knife doesn't start off upgraded, so Lara has to return to cut open the two barriers there.

At plane wreckage site, Lara has to upgrade the knife again, but it goes immediately to finely crafted knife if that is what she had before. Once she gets the bow, she gets all of them. 

After doing the jungle "loop" back to plane wreckage camp, fast travel is enabled, and since Lara had upgraded knife, I fast traveled Lara to Cozumel's Tidal Caverns camp to open the two barriers, and noticed that the rifles and shotguns became enabled, but not the pistols. I was able to upgrade the bolt action rifle there. Going back to jungle, the rifles and shotguns were gone. Once Lara is done with the soldiers on the way to Kuwaq Yaku, she gets all her weapons back. By this point in my play through, Lara is maxxed out on most inventory, including gold ore and coins. The coins can be spent on buying weapons and outfits from the "other" paths.

Completion of a tomb only shows tomb complete, without the skill pop up if Lara already has the skill from the first run through.

 

 

 

 

Edited December 12, 20187 yr by rcgldr
update info

Good to know. I'm hoping to finish this walkthrough and dive into NG+ over Christmas break.

Yes, that's what I found, I had 18 points or so spare at the start and had another four I think by the time I got to a place where I could buy skills so got all of them very fast.  I didn't find the NG+ thing that enjoyable as a concept, given how lethal Lara is anyway by the end of a normal game.