I think it is a case of trial and error. You are looking or someone who doesn't hate what you write, because it would be a slog for them and not beneficial for you if you are constantly being told things aren't good. But you need it to be honest enough that they will tell you if something doesn't work and explain why. I have had some people read who aren't sff writers/readers, but this has definitely been less useful, as they don't always know sff conventions. Similarly, within the genre there can be such a breadth and we need to try to match that.
I dont read epic fantasy much, and i am not a fan of it, so as a beta i am worse than useless. I would be looking pace, where they want depth of description. Similarly, hard sci fi, i would have no idea if the concepts are viable, nor do i read it and know the conventions.
In terms of when, i find it most useful at a nice, strong second draft stage - says she frantically editing wip to get it to that stage as i go - but a readthrough of he completed version, preferably by a new pair of eyes, to see if the changes have worked is really good.
Oh, and its worth considering a professional edit imho, when i sent wip1 for this, despite oodles of beta reads, the review by teresa edgerton threw up so much, not just for that book but for my subsequent work. For wht i got back from it, it was well worth the expenditure.