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I like past for a first-person narrator that's explicitly recalling things. It lets them chuck in asides of the "as I later learned..." type when you want a little extra exposition. (ex. "I later learned the the kronkweschel, or at least that's the best I can put what they call themselves in our letters, express emotional subtext by movements of their vestigial gills, instead of varying their tone. Probably would have died if one of them hadn't stepped up and flared their gills for me right then.")

Past does usually lock you out of killing the narrator, because it's a foregone conclusion that they survive long enough to look back at their past, although you can pull the twist that the story up to a certain point has been a recording/memoir/journal/etc. that the actual main character has been reading.

Present is tricky to handle, and is usually only done for full-bore stream of consciousness first-person, where you want to make the reader feel like they're actually inside the head of the narrator while everything's going down.

There's an odd edge case, though: you can write first person past tense as basically third person limited past tense except you use "I" for the pronouns and never mention anything the narrator doesn't see or know at that point in the narrative. ex. "I walked through the door" vs. "If I'd know there were gonna be fifty guys with tommy guns on the other side of that door, I wouldn't have opened it". Both are in past tense, but only the second one has the narrator using information they got after the action they're describing. You can pull this style without doing the "I'm narrating my memoirs" approach, if you're sure to stay consistent.