Favorite sprite... that'd have to go to the Wyvern class frigate, and not just because it's got my name on it.
Honorable mentions go to Dragon, Wyrm, Raptor, Germany, and the Alien Mothership - the last not so much for the base hull, as for the way it looks with all drones deployed.
(Not to say the rest aren't awesome too; these are just my favorites.)
Favorite hull to use in play... Dragon. Yeah, okay, the Germany is indestructible once you have a high enough character level, and there are other ships with more firepower, and blah blah blah; the Dragon is just fun.
Favorite weapon is the particle cannon. Sure, there are other guns with better damage, or better flux efficiency, or point-defense capabilities; there are even a few with better range. But particle cannons are cheap and accurate (once you've got a good level of gunnery implants) and effective, especially if you can mount a number of them.
Honorable mention goes to the lowly microlaser; it may not even be the best PD weapon out there - but it's the only gun that will reliably deal damage to those annoying teleporting alien frigates. (Assuming cruiser+ hull with a range boosting hull mod, anyway; otherwise the pests like to hang around just outside of microlaser range.)