You do not want to run cable in conduit other than brief runs to protect it from physical damage. I presume this conduit is also underground. If so, no matter how "waterproof" you think it is, the code considers it a wet location (believe me it WILL get wet). You must use appropriate wet rated conductors (THWN).

Your surmising is right that you must run 4 conductors (HOT, HOT, NEUTRAL, GROUND) to the subpanel.

How is that wire sold is it as individual wire ? And should I go with # 10 or 12

This post was edited by cbubbagump on Thu, Aug 22, 13 at 9:10

Yep, you typically find it on a spool. Most places (even the home centers) will have dual marked THHN/THWN which will be legal here. The down side is you will need wire that is not white or green for the hots, white for the neutral, and green (or bare) for the ground.

The wire sizing depends on what the load in the barn AND the distance involved (and the wire size also determines the circuit breaker size to be used).

Your Square D Homeline panel you purchase doesn't include a ground bar. You must purchase ground bar kit PK7GTACP separately to complete the installation. It should say that on the outside of the cardboard box your panel came in. The green bonding screw that is included with your panel is not use. You will not be bonding the insulated neutral bar to the enclosure. Neutral wires (white wires) only to the insulated neutral bar. Grounding wires (green or bare wires) only to the ground bar. You will however be using the green mounting screws that come with your ground bar kit to bond the ground bar to the enclosure.

Will you clarify what you meant about '120 from 240' in the panel?

I did purchase the separate ground bar and installed it in the panel . Is this wire suitable for my purpose Menardî SKU: 3691937
I am going to connect the ground wire from the outside ground to the ground bar . The white to the neutral bar and red and black to each of my hot lugs . That would take my 240v line coming in and give my panel 120v that's what I was referring to.

Right and while you didn't specify it, the ground from the feeder needs to be connected to the ground bar (or another installed ground log) instead.

The instead should be within the parentheses above. I wasn't attempting to say you should not connect the grounding system (rods) to the panel.