No budget? Alright, let's have some fun.
My interpretation of trance is something with hard-hitting, clean frequency extremes. Shrill trble or anemic bass would ruin it. These can come somewhat at the expense of a natural midrange, if need be.
I'd go with the Audio Technica ATH-L3000 headphone, first. That can is a lot of fun, and I doubt you'll ever feel like you're missing out.
As to amps, you have quite a few choices. A balanced Beta 22 wouldn't be a bad idea, but I've heard that the L3000 don't benefit much from balancing, so I'd go with a single-ended amp. I think the Luxman P1 would likely be a very tuneful match, and would give you the impact you're looking for.