I have a simple light switch I want to get hooked up but not 100% sure if it will work. The switch has 1 brass screw on each side and 1 green screw. I read that the black/red wire should go to the brass screw while the white should go to silver, however, this switch has two brass screws and I have 1 black wire and 1 white wire.
Switches don't have silver screws (unless they have brains inside)
Your rule about "black to brass, white to silver" is a good rule of thumb for how receptacles are wired. However, since a "dumb" lightswitch simply connects terminals to other terminals, it needs no connection to the neutral wire at all, and thus has no silver screw on it to begin with. "Smart switches" and some other devices such as many sensors and timers, though, require neutral to work so that they have a reliable source of power for their own innards.
Furthermore, prior to the 2011 NEC, electricians were freely allowed to take advantage of the fact that switches don't need neutral by running an "old style" switch loop using /2 cable as you see here. The white should be the always-hot coming down from the fixture box and the black should be the switched-hot connecting the switch to the fixture, but that rule was not always obeyed in older wiring. It doesn't matter from your standpoint, though; simply wrap the white wire with black electrical tape to denote that it's not neutral, then connect white and black each to a brass screw on the switch, button everything up, turn the breaker back on, and enjoy! (There appears to be no grounding wire in your box, so there's nothing to connect to the green ground screw on your switch.)