Emergency contact type of phone or all singing all dancing smartphone?
For the former, a £10 Samsung from Argos in a plastic bag with a pay as you go sim.
For the latter, I've got a Sony Xperia Z3 compact. It's not compact, it's bigger than an iPhone. But it has ridiculous battery life (can log a 24 hour event using Strava), has a good camera and is fully waterproof.