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When wiring, in this case a Les Paul in standard configuration, whats the different types of wire you would use to wire,

Any ground connection,
Pot to pot connection
Switch to pot connection
Switch to output jack connection

The wire i have is unshielded polywire, cheap and thin.
2 conductor shielded wire
Single conductor insulated wire
Single core braided and insulated wire.

What wire would you guys use for these connections?

I almost always use braided (multi-strand) insulated wire for control wiring, even for the ground connections. I usually try to shield the control cavity with copper foil, tho I don't always have any handy, so some are shielded amp; some are not.

For a Les Paul, the switch-to-pot connections should be shielded insulated wire, you could use your 2-conductor shielded for this, try to avoid ground loop by connecting the shield ONLY to ground at the controls (pot) end. You may want to use this for the pot-to-jack wiring too, if the run is long.

I would avoid using single (solid) conductor wire, it won’t flex well and may break, though I see it used a lot for grounding connections, i.e. connecting the metal pot covers.

One mistake I make frequently is that I leave shielded wires too long, and the shield then accidentally connects to some signal point, amp; I get a short. Keep those shields tidy!