Well, the minimum you need is just... a cable. You can get mic input, PTT, +8V, and ground off of the mic or accessory connectors on the radio, and audio output (if needed; I gather you just want to listen on your HT) from either of those or the external speaker jack. If you put each signal, along with ground, on one pair of the CAT6, and wire up to a microphone connector in the house, it might work 100% okay.
If the cable is too long, the voltage drop might be too much to allow the PTT to key reliably. In that case, you can use a simple NPN transistor switch to help it out — collector to the radio's PTT pin, emitter to ground, one side of your PTT pair to base, and the other side to the radio's +8V through a suitable resistor (small enough that your PTT works, large enough to keep the current reasonable. Maybe 0 for a very long run.)
If your transmit audio is too noisy, or just too low, then you might need to boost the levels on the cable. This is somewhat of a pain, because it appears the 706mkIIg comes with, and expects, a condenser-type microphone. Two routes suggest themselves:
Switch to a dynamic microphone, buy or make a simple mic preamplifier, and connect it between the mic and the cable at the house end. On the radio end, use the MOD input of the accessory jack, and not the mic jack. Crank the preamp level up to a point which brings your voice well above any noise, and then if that level is too much (overmodulates the radio), use a resistor divider to ground to bring it down as needed.
Keep using a condenser mic. Use audio transformers at each end of the cable for isolation. Provide 8V bias for the mic, and a DC-blocking capacitor in series with the microphone. You may or may not still need a preamp.
Speaker (if you choose to wire it) will probably be fine, but if the levels off of the mic or accessory jack are too low, then the rig's "external speaker" jack should provide considerably higher ones :)