Last I remember reading Cilff liked the beyerdynamic 880 pros and those are 250 ohms. I bought a pair and I think they are plenty loud for the axe fx. They sound really good especially for the price.
If I get headphones with 250 Ohm will I need an headphone amp with the axe fx?
No. I have the DT880 250-ohm model, and they work well with Axe-Fx. Adjust the output level (OUT1) for desired volume.
I bought the Beyer Dynamics DT880 250 ohm headphones and returned them. They just did not sound right to me. Thin and no bass.