If you currently use cheap ear buds, then maybe another option to consider is something like Etymotic “In Ear Monitors” (IEM)?
Even with an iPad dongle, or with a standard iPhone 1/8” audio out they are surprisingly good.
If you are looking at cans. Then you probably want to select the can before selecting the amp, so that you can ensure the that required output impedance works.
Half the time I use the IEM without a pad, as their noise blocking is pretty good, so I use them like ear plugs. But I also have a few Etymotic ear plugs handy most of the time as well.