Take it from an actual investigator. This one is as simple as it gets. She didn't strangle herself and then he accidentally got himself eaten by alligators. The next clue you find will obviously be the first, but add up the pieces here, if able.
Or, we can wager. I'll give you "the field." If literally anything else happened here that can be proven, aside from he strangled her, then killed himself, I'll quit this and the next board. What do you wager?
Sometimes hedging in a feeble to attempt to appear wise has the opposite effect.