I've been spending the last couple of weeks working on ideas for a couple of quest mods I have in mind. However I'd like to start with a simple mod first. One that allows you to recruit the Old Orc as a follower rather than just being forced to kill him, culminating in a brief questline that is completed when he dies against a Dragon Priest, Ancient or Elder Dragons or against high level enemies in general.

How do I add in a additional dialogue branch that allows me to recruit him?

Start with this - Here is a good tutorial for setting up dialogue.

http://www.creationkit.com/Bethesda_Tutorial_Dialogue

That will get you going in the right direction.

Your idea requires 2 more blocks of work.

1) Follower behaviors - Take a look at other followers to start.

2) Quest. Unless you have made a quest before, I'd suggest you just make the quest ANY enemy that kills your Orc Follower.

You'll be able to find more information on creating the quest than creating a follower.

You'll also want to get a BSA browser so you can extract voiced lines and then create your own dialogue using the Orc voice. Even a simple response like "Okay." requires that you create a new dialogue for that character.