If you are using a 5 V adaptor, a 1000 ohm resistor (known as 1k) will probably make the LED a bit dim, but that's fine if you can see it OK. If the 5 V adaptor is DC, you don't need a rectifier.
You probably only want an SPST switch, if you want both of the LEDs to light at the same time. You can use a DPDT switch as a SPST switch, but only connect to two terminals of it. I've seen several instances of people making things far more complicated than they need by having switches or relays with lots of terminals and somehow thinking that they have to use all the terminals.