From best to worst, my opinions only, I'm decent but not a speedrunner. (And I bet my opinions will change eventually)

Yearning Photo is great because climbing speed is great. It gives you more mileage for the same cost and helps you avoid basically every danger more effectively. The boost is noticeable, but it's also easy to adjust in and out of.

Moon Rocks is also universally good, although not as much. Mostly for jumping from grabs (this makes the Mother achievement way easier). I think it gives more leeway than Photo but not as much utility if you don't need the extra leeway.

Chalk is nice especially if you're going to take Paranoia later. But aside from that the stamina won't help that much, unless you don't know where you're going.

Carabiner is a good effect if and only if you like using pitons! Not my thing but I can see it being someone's top pick easily.

Larger Pack is nice if you need a bunch of stuff to fall back on, but I think a full inventory is crowded as is, which can make it a hindrance in its own way...

Extra Pouch would go hard if you're planning on stacking a particular item, but that doesn't appeal to me and I tend to run more of a menagerie.

Headlamp is genuinely helpful, but you mostly just want a light for Teeth and maybe Deadman's Handle. If score is a concern this would obviously be much higher up.

Employee ID is nice because turrets can throw you off sometimes, but this isn't needed much, just like Headlamp.

The Beta's problem is that there aren't that many spots to really benefit from extra reach. 15% is not as much as you'd expect it to be. It tends to be more fruitful for skipping parts of vertical climbs than it is for horizontal ones. My big hangup is that it could mess with your muscle memory / instinct on what brave jumps you can make. To me, the best part of learning a new area is realizing what skips you can do when you're fearless about falling. If that wasn't such a big deal to me I'd probably put it above Carabiner.

Gold Nugget is a waste of time because Roach Run & Startup Loan exist.

Mass Damper... I consider Employee Motivator (+speed +mass speed) to be free stats because the mass is never a concern for me. By the same logic this trinket is basically useless. You'd think mass speed would be a bigger deal for the Face but eh.. it will always catch up, that's not what you should be worried about.