I drop Goblin Ringleader on first strike damage...does his ETB ability resolve, putting more goblins in my hand that I can then drop for "normal-strike" damage?
Creatures with first strike or double strike cause there to be two separate combat damage steps, one for first strike combat damage and one for regular combat damage. Players receive priority at the end of these steps and may cast spells and activate abilities.
That said, you are correct. Warren Instigator hits in the first strike combat damage step, and his ability triggers. You put Goblin Ringleader in and its ability triggers. Warren Instigator connects a second time in the normal combat damage step and you can put another Goblin creature card into play.
You put Goblin Ringleader in and its ability triggers and resolves*.
Just for reference and because I spent the last 15 minutes looking for it, here are the relevant rules:
510.3. Third, any abilities that triggered on damage being assigned or dealt go on the stack. (See rule 603, "Handling Triggered Abilities.")510.4. Fourth, the active player gets priority. Players may cast spells and activate abilities.510.5. If at least one attacking or blocking creature has first strike (see rule 702.7) or double strike (see rule 702.4) as the combat damage step begins, the only creatures that assign combat damage in that step are those with first strike or double strike. After that step, instead of proceeding to the end of combat step, the phase gets a second combat damage step. The only creatures that assign combat damage in that step are the remaining attackers and blockers that had neither first strike nor double strike as the first combat damage step began, as well as the remaining attackers and blockers that currently have double strike. After that step, the phase proceeds to the end of combat step.