Depends what you’re trying to achieve.

CMOS noise, especially deep in the shadows, sort of clusters in strips. It can be a giveaway or just a slightly undersired look compared to “film” style grain which has some interesting properties on it’s own but is easy to simulate at useful scales.

Shoot to get the picture. If going higher ISO doesn’t hurt your result and makes it easier to get the shot, then go for it.

Careful when adding noise though - I tend to avoid it because it’s not “truthful”, but we’re all just making pictures here. It may not make sense when looking back after a few years

Try both fuck it

Take the best shot, then add grain in post

If I’m going for the grainy retro look for some lowlight photos would it make sense to keep ISO low and add grain in post, or would the grain from turning up the ISO give a different kind of grainy look

“Grain” is a property of film, not digital. If you want to have a “film” like grain, the best option is to add it in processing or post-processing stage in computer - you have infinite options then to define what kind of uglyness you want.

Generally one should capture as much information as possible - it’s always easy to make low quality (for example the retro look you’re after) from high quality information, than try to get a low quality shot right away on the camera and hope it’s the right kind of low quality ;)

To collect lots of information, you should collect as much light as possible. Thus go for as long exposure and as large aperture as possible (and then you can set the ISO to as large as possible without burning anything, though often it’s much more practical just to let the ISO float automatically.)

You can simulate grain in post but high iso is just noise and not grain.

Besides the information already posted here about noise and grain, I might have to add something to the way you seem to perceive ISO.

Increasing ISO while keeping the same light-conditions would rather decrease(!) your noise. There is a lot of misconceptions regarding ISO. The ISO (in digital photography) is simply working as a gain for your light, resulting in higher signal and noise levels. BUT, the noise you see is not dependend on how high your noise level is. It depends on how much more signal than noise you have. And as long as you don’t blow out your highlights, your signal to noise ratio stays the same. But if you shoot underexposed you decrease your signal to noise ratio and that’s why we think raising ISO adds noise. Because in that case we start using higher ISO and realize that we start seeing the noise. But compared to postproduction the camera still works with far more signal than in the resulting raw-file, meaning that increasing the ISO will introduce less noise than increasing the exposure of the Raw-file and shooting with high ISO results in less noise than increasing it in Post-Production.

Don’t believe me? Try capturing the same scene normally exposed with high ISO and than underexposed with low ISO and raise them to the same level of exposure in postproduction.