I don’t think there’s any one element that he is particularly good with. Sponsored By is a great skill, but it’s a capstone, and we’re talking about a level 10 toon at present. That’s a way off yet, and I saved that whole tree for last with my Timothy. Money is Power is also a great skill, and in that tree, but you’ve gotta wade through two tiers of junk to get to it.
One of the really great things about Timmeh, is that you don’t feel like you have to pigeonhole him into a specific element or gun type. Sponsored By should be the ultimate expression of that. Tote what’s comfy for you. Jack’s skills are more about being able to sponge bullets, I think. And he’s a grenadier, too. Early game, that might not be a bad avenue to explore. He has COMs that grant mad grenade damage bonus (over 50% at end-game), and skills to improve his grenade performance. Add in a Bomber oz kit, and he can be a nade chuckin’ evil genius.
So, watch out for good shields (he has good skills for shields, and good COMs too) and good grenade mods, and stick to whatever weapons you like best. Early-game, it’s pretty easy goin’, and you can pretty uch do what you want without worrying.