Yikes, this happened on 2 or 3 of my switches but I noticed before soldering either pin. I was able to pop them back out and straightened the pin before soldering it to the PCB. I haven't experienced any damage to the PCB from the switch pins getting squashed.
And for solder, I've always used 60/40 rosin core for keyboards. For this project, I ordered some "fancy" Kester 63/37 rosin core. Not sure that the composition of the solder made a difference, but thinner wire is easier to work with. I considered picking up some flux too, but I read that you probably won't need it unless you're desoldering and I did not miss it during assembly.
63/37 solder has a slightly lower melting point than 60/40. If you're soldering by hand you won't be able to tell the difference but in industrial settings where a higher melting temperature means you have to spend more money on power, they go for the one with the lower melting temperature.
It's not just about the melting point. 63/37 is an eutectic mixture which means that the whole compound melts at the same temperature in a homogeneous fashion, whereas 60/40 has a plasticity range, and this is almost definitely a difference that you CAN tell intuitively by feel, that is somewhat separate from the fact that it's a lower melting point.
In short, 63/37 mixtures 'feel' like they melt instantaneously whereas 60/40 'feel' like the mixture is more sluggish, appearing more gel-like while it's in its melting point range before reaching its liquid phase, and this manifests in a very real, easy to feel difference. 63/37 solder mixtures are easier to work with not because they're 'fancy', but because of the metallurgical nature of the particular mixture which lends itself to being easier to handle, especially if you're working with low cost, casual style soldering iron which may not have the best temperature sensing or control.
Do yourself a favour, use 63/37 mixture, it will make your life easier (doesn't have to be Kester solder, although I do prefer using Kester brand due to their excellent flux formulation which wets out the pads and contacts in a pretty even and well controlled fashion which makes for a nice consistent joint. If you're using the Kester 44 formulation, I recommend wiping off the flux residue after soldering because they are quite dark in colour and look a little ugly (supposedly non-corrosive though, so I suppose it's not technically mandatory)
