Gene Hamburger
Hercule Poirot
^^ Claude!
Harry Dresden, John Constantine, Bob Howard, or John Taylor.
Heck, just have all four of them team up.
My death might as well be a precursor to the apocalypse!
I’m 59 and I read it in a copy of Ellery Queen’s anthology 101 Years’ Entertainment which I found at my grandparents’ house. I’ve read a couple of Futrelle’s other Thinking Machine stories. They’re not nearly as good.
I think the best Poirot stories do not involve the captain.
IF I can figure positively in a Devil’s Cherry hallucination, then Patrick Jane.
If I will be able to watch and enjoy the investigation, than Columbo. Or Monk. Or Shawn Spencer, Gus, and Lassie. If I can haunt Lassie.
If I want vengeance, then Leroy Jethro Gibbs. Serge Storm and Colman would be entertaining, as Silenus said, but just a bit over the top. And, as dead, I couldn’t enjoy the communion of substances with Colman. Anyway, Colman’s lack of thinking would drive me crazy. My ghost might conjure up some plaid for Serge, though, just for the fun of it.
If my ghostly form can assemble a physical manifestation and create an “affectionate” interaction with the investigator, then definitely Patrick Jane. If it would be possible to detach him from his fixation on his dead wife.
I agree, except for “the ABC murders”
Yikes.
But the question was whom would I want to investigate my murder, not which stories were the best for that character.
So I reiterate: Poirot AND Capt. Hastings. No, I do not have red hair!
By that logic, I agree with the poster who picked Lennie Briscoe — because, hey, if I’m going to die anyway, the best I can maybe ask for is a wry quip over my dead body, and rules being bent to find the murderer and inadmissible evidence then being tossed out, followed by an interesting twist brought to my family’s attention, followed by heartfelt speechifying from Jack McCoy, followed by the smirking killer being acquitted moments before he’s gunned down on the courthouse steps.
I genuinely wish I could put that in my will.
190 posts so far, and no one has mentioned … Horatio Caine? [Whips sunglasses off dramatically.] 
If I’ve just been murdered most foul, I don’t have a whole lot of interest at the moment in investigating anyone, do I?
[even if they are a dective]
Burke.
He’d make sure that my murderer got what was coming to him if he deserved it.
Saga Norén.
Susan St. James.
Detectives Martin Riggs and Roger Murtaugh.
Accompanied by explosions, gratuitous swearing, wisecracks, car chases, a truly astonishing body-count and an 80s saxophone soundtrack.
Sorry, at this point, they’re both too old for this shit. 
The fiesty-cheeked Angela Lansbury.