The first real interceptor is, well, the Interceptor. MiG
might work against cultists, but those have similar-tier craft themselves after a while. If not even better than yours, actually. You also need Avalanches / Heavy Stingrays to actually make the craft work as it should and not be a glorified cannon platform.
Unlike the original, missile and cannon slots (and light vs heavy missile, and laser, and extra equipment ...) are 'hardcoded' to be different. So no changing between dual cannons and dual Avalanches any more.
Missile research should be pretty self-evident.
The big and largely
undocumented difference between aggressive and cautious (and standard) is that your fire rate goes up the more aggressive your stance is. So it's usually better to be aggressive, to minimise damage and the chance that the enemy craft escapes.
If you outrange the enemy, cautious might be usable. That of course assumes you also either out-speed the other party, or pack enough firepower to shoot it down before it escapes. Maybe tractor it, but that's lategame tech.
Standard mode is mostly for when both/most/all your weapons outrange the enemy, cautious is when only your best one does.
As to the ghost missions, haven't played them myself. But I recall that one of them had one enemy hidden deep underground, so you either need to dig down, or just grab whatever you came for and bail. I imagine the latter is the intended course of action.
In addition to tasers. lasers looted from MiBs and cultist ectoplasm weapons should also work against ghosts.
Crosses don't persist post-mission, since they're powered by (the residue) of that priest's faith.