ditto on sunny 16. i used to shoot with an M6 but would constantly fiddle with speed and aperture to get the "proper" exposure the meter would indicate. I started shooting with TLRs that had no meter and began to try and use sunny 16. after a while I could meter by eye fairly well, but still I would check exposure with a meter. then I got an M3 and shot 2 rolls completely metering by eye. zero missed shots due to bad exposure. it helped with confidence.
nowadays i shoot with an M4, only meter by eye. try to practice sunny 16 and pay attention to the aperture/speed combinations you are using in each light situation, most of them will be extremely frequent, and the new ones you will run into can be estimated using your previously metered references. it will be very rewarding and it's not such a big deal: film can take over/underexposure very well. i've once exposed the last 3 frames of a roll as 800 (what i usually shoot with), when i took the film out it was an 100 iso film. surprisingly, the shots were very useable after a scan. film lattitud is VERY forgiving.
ps: the iphone meter app is pretty good, i have it too, but i end up hardly using it as i got used to metering by eye anyway.