look at the inside of the lens cap, filter thread size already stated there.
My lens hood is always on, day or night, once the camera is out of the bag, the only time I remove it is when I have CPL filter on or it gets in the way when I need to shoot very close to glass window.
as mentioned.. you can find the size of what lens filter to get on the lens itself.
if you buying filter.. bring the lens and get it fixed in the shop.. Better that way..
As for lens hood. I leave it on everytime. Like what Catchlight says. The only time i remove it when i have a CPL filter on or when the lens hood really gets in the way..( for some lenses.. the lens hood can be big )
the cheaper the better
just google for CPL, ND filters, have a read on what they do and see if u need them for the things you shoot
as for UV filters, there are 2 camps of thoughts, see you prefer which one
lens hood most of the time i leave it on also when keeping the lens just revese it
A7RII| FE 24-70mm ZA | FE 16-35mm ZA | FE 24-70mm GM | FE 50mm | FE 70-200mm GM
lens hood reversed when in storage and lens hood is on when in usage.