Vaegir and Khergit lords should build agility because agility is useful for ranged combat and also some other skills, and these two factions rely on agility tactics, while all the others rely on strength tactics. You may trade later if you want, but you’ll win a lot of denars winning battles. Strength gives you one more hitpoint, so you can take more damage without dying, and the skills you learn by having strength are VERY useful to warriors, and you want to be a warrior on Mount & Blade. So, you need to be a good fighter to be good in this game. Mount & Blade is mainly a game about fighting, winning battles and wars and taking more lands for your kingdom and for yourself. Vaegir lord main characters should build strength and agility and charisma. Actually, for Vaegir I recommend building three stats and this is the only case.
Yes, Vaegir lords could build either one. You should build agility if you plan on being either a Khergit Khanate lord or a Vaegir lord. You should build strength if you plan on being either a Swadian lord, a Rhodok lord, a Vaegir lord or a Nord lord. Don’t build intelligence, I think intelligence is useless for Mount & Blade (classic) main characters. One should be either strength or agility, and the other should be charisma. Some may disagree, but my opinion is that YOUR main character should only focus on TWO stats.