I assume you are only looking for options by going from belay to belay (as opposed to continuous securing like going on taught rope).
Method using half-ropes:
You tie in on both ropes, your partners on a single one each. They belay you normally on both ropes until you set up the belay-station. Then you secure them using a Munter hitch or a tuber like system to belay them. Using a tuber is preferable, as it autoblocks and does not twist the ropes around each other. They can climb simultaneously, just having to keep a minimal distance, which depends a lot on how fast the rope is pulled in by the belayer.
- Both partners can go at their one pace (as long as the faster one starts first).
- One falling does not affect the other.
- Two half ropes are heavier than one single rope.
- The belayer has two ropes to manage
Method using one single rope
You obviously tie in on one end, the partner which climbs best on the other end. The weaker partner ties in at a save distance from the end. The exact distance is always a compromise between available rope length and safety margin between climbers. The one in the middle can be tied in using a variety of knots, I prefer an overhand secured by a double fisherman's knot. The weaker one starts climbing and the second one follows as soon as the rope in between them is almost taught. If the first falls, this does not affect the second. But if the second falls, he will pull the first off the rock.
- Only one rope needed which is lighter than half ropes.
- The second has to climb exactly at the pace of the first.
- The second has to be fairly competent as a fall will pull off the first.
- The usable rope length per pitch is reduced by the distance between the partners
Method using two single ropes
You tie in on one end of the first rope, one partner ties in on this and the second rope. The other ties in on the other end of the second rope. After you led the pitch the first partner climbs it and clips the second rope into the protection. If the pitch goes sideways and he is insecure, the second partner which is still down at the previous belay can belay him from behind. Thus falls with swings can be caught. After the first partner reached your belay, the second one climbs the pitch.
- Very easy to handle.
- Perfectly save, especially in traverses for the first partner.
- full rope length available for pitches.
- very slow (nearly twice as long as with half ropes)
- heaviest setup as you carry two full ropes
I would always prefer the half-rope method, its the fastest and save. And the additional weight should not be an issue, after all you are three climbers. If you really do not want to handle two ropes (though it is very easy, just try it out) I would recommend the method using one single rope. The last method is really just in case you need the rope length, and both your partners struggle with the grade you are using or you are insecure handling two ropes (again, thats a none-issue). And keep in mind: You are always a lot slower in a three person rope team than with two.