During the events on [Virmire] your actions will determine whether Captain Kirrahe survives or perishes.
Choice: Keeping Captain Kirrahe Alive
This is perhaps less of a “choice” and more of a competence check. After rendezvousing with Captain Kirrahe on Virmire you’ll have to go deal with your krogan problem, after which you’ll need to talk to Kirrahe again, lend him one of your human squadmates - either Ashley or Kaiden - and begin a coordinated assault on the enemy base on Virmire.
Once the assault on the base begins you’ll have several objectives you can pursue to help Captain Kirrahe’s squad. Only one of them matters when it comes to keeping Kirrahe alive, and that’s destroying some Geth Flyers outside of the Virmire base on a Refueling Platform. Kill any Geth Flyers you find and destroy the fuel tank and you should get an update. If you do this, Kirrahe will survive the mission, if not, not.
The Triangulation Tower, Satellite Uplink Tower and drawing the base’s security to you are all irrelevant to Kirrahe’s survival.
For a relatively minor character, Captain Kirrahe plays a fairly outsized role in later events. As for immediate consequences, the only one you’ll really see in Mass Effect 1 is on the Normandy immediately after Virmire. If Captain Kirrahe survived you’ll be able to purchase items from Commander Rentola, including the Serrice Council and Sirta Foundation licenses. While noteworthy, you can purchase both of these from other merchants.
While Kirrahe doesn’t make an appearance in Mass Effect 2, his contribution to events in Mass Effect 3 is significant. If he’s alive he’ll make an appearance during the mission Priority: Sur’Kesh, otherwise being replaced by another Salarian, Lieutenant Tolan.
Later on in Mass Effect 3, Kirrahe is one of two possible characters who can save an important NPC’s life (the other possible character being Thane).
Finally, if Wrex is dead and Kirrahe is alive, he may appear in a scene during a late-game battle on Earth.