Higher DPI = more precision, but the mouse's native DPI might also matter.
Also this: https://youtu.be/NUiGkDB_48s

you need at least enough dpi to move by one pixel
for a 1920x1080 monitor, at 90 fov in source (which is about 106 true horizontal degrees on 16:9):
1920 * (360/106) / (inches per 360) = pixels per inch (so just make sure your dpi is higher than this; for 4.5 inches per 360 you're gonna need a high value)

and I've heard you don't want to make it too too high because your mouse can jump or not move on fast swipes (not sure how true this is, but you never see CS pros play on high dpi--more than like 1000--and low sens)

It doesn't matter hugely
Higher DPI can increase accuracy but it also has a lot of problems with many sensors.
Some mice have issues on non-native dpi although this isn't the case for newer ones normally
Some mice (a lot of 3090 mice) have jitter on higher dpi
3988 mice have smoothing on higher dpi
A lot of mice don't actually reach the advertised dpi at higher steps with the actual dpi starting to fall off as you get higher.
In most cases it wont make a huge difference. Use something you feel comfortable using on desktop that's not crazily high ingame.
you can also use http://www.funender.com/quake/mouse/index.html to calculate your true sens and your "estimated useful dpi". Think of this as a minimum dpi to use, as you shouldn't get pixel skipping above that.

the most common sense is 400 for cs pros, however there are alot of other numbers so i feel like it really doesn't matter

i have to use 3200 otherwise my mouse fucks up nice mouse
zowie ec something is my mouse btw

AFAIK, using low dpi was common b/c most mice's native dpi (the dpi with little error) was pretty low. I think the Zowie FK1 works fine on every dpi step, but most people just stick to 400/800 b/c they're used to it, this of course depends from mouse to mouse.

A high DPI with a low sense tends to result in negative acceleration. It's not an issue in TF2 where you can turn on raw input, but other games that don't support it will end up slowing down your mouse movement when you move it too fast.

Most mice work at 800 DPI, and that's usually one of the native DPI steps for gaming mice, so it's a good starting place.

That formula is a bit rough, because in FPS games you technically don't aim in pixels but angles in an inverted world transform matrix. Hence the "estimated useful dpi" that was already linked gives a more accurate result as it compares the width of a single pixel near the crosshair to the minimum angle you can move with the given sensitivity. If you go below that number of CPI you might skip pixels partially.

That is all explained in more detail here: overview of mouse technology

CPI =/= precision, it's just the speed of the cursor, meaning how many counts the mouse sends to the PC for every inch of movement. The higher precision in games comes from lower in-game sensitivity which reduces the angular change per count.

Also in my experience there is something like too much CPI/too low in-game sens where it starts to feel floaty. For my low sens of 60cm/360° I prefer 400 CPI@1.8 because it feels more controlled than 1800@0.45 for example.

I might have used a wrong word, but you could just watch the video I linked to see what I meant.

dots per inch = degrees per inch = sensitivity (that thing there's a console command in every game for)
"more precision" from a specific dpi setting is nothing more than placebo

see #4 and #9
+ look up the specs of your mouse

I understood what you meant, I just wanted to clear that part up because the video has mistakes. What he presents there is just the effect of lowering in-game sens to 0.3. Keep 400 CPI, use 0.3 sens and you won't get staircase movement either. Also what he shows there is pretty much irrelevant in a real world scenario because the area in which the staircase effect happens on normal fov settings is less than one pixel. There isn't an obvious negative effect to doing that, but personally I don't like how a very low in-game sens feels, the movement becomes floaty. Ymmv on that, some might prefer that feeling.

Also the term of native CPI is misleading in that video, because the sensor used there is the 3310 which has native steps in 50 CPI increments, Zowie just limits them due to not wanting to offer software. The whole "native steps" debate comes from the old age of A3090 (or older) sensors where you had to apply some trickery to gain steps between the native 400, 800, 1600 etc.and is not really applicable anymore.
It's still correct that you should not use a too high CPI, but that has nothing to do with native steps and is only because even the best CMOS sensors still jitter at settings higher than 3200. Depending on type of sensor this threshold can be higher or a bit lower even. For most sensors if you don't want smoothing you should even stay <=2000 CPI.

EDIT: my bad, he explains some of that at the end of the video.

this is just not true though, if i had a mouse with 1 dpi then it would be incredibly imprecise because the majority of the movement of my mouse wouldn't register a new angle. obviously with actual, realistic dpi values you very quickly start getting diminishing returns as you increase your dpi, but that doesn't mean that all dpi settings give you the same level of precision

I USED low dpi and high sens and got curious like you did and read on this https://www.reddit.com/r/GlobalOffensive/comments/2fgai3/the_mathematical_difference_between_high_dpi_and/

Now I use high dpi with low sens and the first time I switched, it actually felt surprising smoother. But, like a lot of people have said, it depends on how well your mouse handles dpi. I use the 2016 zowie ec2, so I'm good. There's a mouse reviewer that I watch that also made a really good video on this topic.
https://www.youtube.com/watch?v=jss9Zo37MCQ

These arguments are always pretty silly. It's just like the "high vs low sensitivity" arguments. One is not objectively better than the other--it's just different. It's true that low DPI + high in-game sensitivity will result in what could be called a small dead zone. It's true that high DPI + low in-game sensitivity can result in more precise mouse response at the potential cost of your mouse picking up tiny involuntary movements. What's the bottom line? Try them both out. Nobody but you can tell you what's right for you. Pick something and stick with it if it feels comfortable to you. If it doesn't, change it up until you find something that is comfortable.

Many of the top level CS players who were around for 1.6 still use low sensitivities and low DPI settings because it's what's worked for them and they're used to it. Newer players come in with medium to high DPI settings and/or sensitivity settings and it works just fine for them as well. Top level players switch to different teams and are then forced to use different mice occasionally. What happens? They get used to it and they're just as good as before. It's all about preference and comfort. It would be very unusual for a mouse or keyboard setting to improve someone's game by more than a few percentage points, and even small improvements can typically be attributed to "I made this change and now it feels more comfortable than before".

Pixel skipping doesn't exist in FPSs. Skipping over models matters, but pixels are purely part of putting the gamestate on the screen.

Just don't raise your ingame sensitivity setting above a level that makes it hard to put the crosshair on top of still targets while you're strafing in the game you're playing. If you need to set it higher than that for comfort reasons, increase your DPI instead, or use (gasp and shock) mouse acceleration.

If 4.5 doesn't make it difficult to aim at models while you're strafing, and your mouse runs better at 800 dpi than 2400 dpi, then even that is fine, despite the "pixel skipping".

I feel like I aim worse with my fk2 on 1600 and with .5 sens than with it on 800 and sens 1. Placebo is more noticeable than any effect the settings actually have on the game.