Honestly, the whole thing where you're allowed aircraft autocannons and even infantry versions if you get lucky, but not RPGs nor C4; the Arrow and Skyraiders but MiGs and Skyrangers are verboten; hell, infantry
miniguns but not anti-material rifles... Seems like a bit of a mess to me and I think a fourth promotion would go a long way towards tidying things up.
As to capturing,
cannons don't have blunts,
grenade launchers do. And these are pretty good unless you absolutely need to not kill the target. Tasers against anything that dodges (ninjas
). There's a whole
thread with suggestions.
Getting off the craft unharmed usually requires smoke if the landing situation is unfavourable. Shields for the front agents is a good idea. A tank or at least tank-like something at the front is even better. AI units can be resurrected with little trouble, so they're good for that. But Solarius is a sadist and if some cultist chucks a grenade or a pack of dynamite at you on turn 1, there's not much you can do against that. Use sacrificial rookies or dogs, maybe.
As to funding, check out the
Ufopaedia. From experience, it seems that the increases are totally random from +5% to +20%, so once your score is good enough to cover everyone's grievances, you're good to go. I use score-based income myself to make it more interesting.
I don't think promotion levels have anything to do with funding. If they're happy, they throw a random increase at you, which should even out over the large number of countries on the list and the time it takes to play the mod.