Transistors: why are resistors needed?
Resistors in this situation are about current limiting. If you applied your 2.3V micro output directly across a transistor base-emitter junction, the transistor would try to draw far more current than is really needed, which would harm either the transistor, the micro, or both. So you put a 500 ohm or 1K resistor in series and this limits the current into the BE junction. The particular value depends on the transistor.

You'll choose your transistor primarily based on the needs of the relay. You need something that can withstand the 6V supply when not conducting, and that can pass enough current to close the relay when it is conducting. Now, you said this was a solid state relay, so this current is probably a lot less than you'd need for a mechanical relay, so you'd probably get away with any garden variety switching transistor, e.g., 2n2222, 2n3904, etc.

Fwiw, there are solid state relays that can be directly driven by logic circuits.