I'd say you're OK with the phone if that's all you've got.
A Zoom (or similar) portable recorder will give you some sort of stereo sound which is nice to have but not essential.

Most important: if possible, experiment to find the best place to make the recording. A large room that's not too reverberant, lack of background noise, and experiment with microphone positioning. Find some way to hold the mic/phone at the right height and distance (a proper mic stand if you have access to one and have a way to attach the mic, or perhaps prop the phone up on a music stand if available).

Getting mic position right is half the battle with recording.