The suction cup method did not work for me at all. Even after applying heat worrisomely long with a hairdryer the glass wouldn't budge. Maybe if I'd had a better or bigger suction cup it could've. I bought a kit from a local store and the suction cup was smaller than iFixit's.
One thing to mention is that it's really hard to try and hold the phone down while pulling the suction cup. And then you'd need a third hand to try and slide a pick in there. Seems pretty impossible for one person to accomplish without something not covered in this guide to be honest.
The solution was to start from the corner that was broken, taking out one bit first and then lifting up next to that, causing the glass to break into smaller sections and just going from there bit by bit.
Also a good technique I found was to use the hairdryer while pulling out the bits which loosens up the glue while you're pulling out a piece (especially a bigger one).
The lens has adhesive surrounding it on the metal frame that will get pressed against the back side of your glass to hold it still. You should either not remove it, or replace it e.g. with some of the adhesive from the old glass. Note that you should use a miniscule amount so that it fits (it's a very narrow ring of adhesive surrounding it on the original). Of course there might be differences between versions but this was the case for me.
Don't clean the adhesive of the sides of the fingerprint sensor.
There is some kind of a filter/grille/grating covering the (what I think is the) focus on the right side of the two black holes. You probably should be careful removing that (I believe it's glued into the glass) and transfer it to your replacement glass if it doesn't have that (none of the replacement glasses in pics/videos I've seen have had it). The glue in it was good enough that I just pressed it down to my replacement glass. I'd post a pic but it isn't possible here apparently.