S - Arts, Leader
A - This space intentionally left blank
B - Tech, Humanities
C - Math, Speedrunner
Arts: You get an extra staff member, a prettier check in desk, and some fluffy feel good stuff where you and Asterion connect over common interests. In the current build this is by far the best background, both crunch (extra stats in work & projects) and fluff.
Leader: I read somewhere something about Nikos' recruitment will be exclusive to leader in future builds. Having extra staff alone elevates leader to S rank; both for the fluff of extra interactions and the crunch of having more stats in work days. That its Nikos in particular elevates it further (god imagine Nikos in the drinking game hah!). Currently (version 0.5) I'd put leader in D rank. Having Argos wrapped around your finger early game is nice, but that seems to be the only current benefit so its almost like playing without a background. When I first played the game and read leader's description, I was under the impression it would help with smoothing over infighting. Like, if it allowed you to put kota and luke on the same team day 1 when they're fighting for example. However everyone gets along too well for that to be a relevant perk going forward unless some unforeseen drama boils up.
I left A rank blank to show the gulf in value between Arts and the rest.
Tech: Now I might be doing my math wrong, but I'm pretty sure the tech background is the only way to get the multitasking achievement. Tech is more valuable to invest in since there are currently two high-tech cost improvements, and only one low-contract cost improvement. Also since Asterion is likely to spend all his time in R&D (outside his obscenely long project), you'll have a lot of contract build up regardless of background. This puts tech above humanities in terms of crunchy value, however both are still very weak in that regard.
Humanities: Being able to subvert Argos early game is the only perk humanities has over its compliment, tech. However due to the points outlined in the tech summary, humanities is almost worthless crunch-wise. There'll need to be a lot more to spend contract points on in the future for this to become worth consideration over tech, let alone arts. If I may be so bold, I would suggest adding unique improvements for tech and humanities to make use of their bonus stats. That alone would elevate them both to A tier. Depending on how valuable or dynamic these bonus additions are, it may even elevate them to S tier. Another thing to consider is the dev's stated desire for this game to be impossible to 100% in any given playthrough. If its say, impossible to 100% tech improvements or 100% contract improvements by end game UNLESS you have tech or humanities respectively, that would also seriously improve their value.
Math: I'm not sure what the benefit of math is supposed to be. I probably missed something, but the only thing I saw beyond dialogue differences that all backgrounds have, math just lets you see what you've stockpiled in tech/contracts/etc so far. Which is convenient that its done automatically for you, but anyone can just keep count in their head or on scratch paper. I've tentatively put this in C tier because I feel like I've missed something. If all you get really is just the resource tracker in work days then this is untiered, aka useless.
Speedrunner: The narrator takes the piss out of the MC and the MC is in kind oblivious; very funny. I like how Argos is confused into submission, even at the cost of not being able to learn his secret. Although the idea of min/maxing dangerous parties for extra rewards sounds nice on paper, in practice I can't see myself bothering with it. Survey resource stockpiles pretty fast so long as you send anyone with a decent survey stat once in a while, so it's not a worthwhile risk to take currently. This background is less C tier and more meme tier, which seems to be the intended goal. I hope for more silliness in future builds. Maybe even 4-th wall sequence breaks that baffle and terrify the whole cast akin to Argos when he first met you.