Is it safe to charge these using a wall outlet (I am in the US)?
It can be made safe to do it this way. You need to take appropriate precautions to protect yourself and anyone in the vicinity. I'm not just talking about protection from dangerous AC voltages (although this is always necessary) but, once the capacitors are charged up they can be very lethal to handle because they will be able to supply massive levels of current and, are not prevented from doing so by a GCFI (ground fault circuit interrupter) as you would get in most household AC installations.
Is it safe to wire them in series after they are charged, or do I need
to put switches in between the pairs before charging so that, once
they're charged, I can connect them without having to wire anything
while they are charged?
It can certainly be made safe but, it's far safer not to have to do this and use a proper capacitor charging power supply or, one of your own design.
I am not super experienced with making electrical things, so I am just
wanting to double check that what I am doing is safe and what
precautions I need to take.
Be very, very careful. Concentrate on finding ways of not directly handling the capacitors and especially not coming into contact with any capacitor terminal. From my own personal perspective (of one who designs high-voltage capacitor charging supplies) I would use a specialist circuit that basically acts like a current limited boost converter and charge the capacitors as they are intended to be used i.e. in series and, keep away from those terminals.