Really budget headphone: Sony Mdr-Zx110 (10 Eur on A.). Light, small, foldable, very good response for the price, short cable, 3.5 mm angled plug with no 6.3 mm adapter, not very loud (98 db/mW), 24 Ohm.
Not so budget headphone: Sony MDR-7506 (95-100 Eur). A classic, foldable, loud, extended frequency response with a little hump at the extremes, long coiled cable.
Or pick the Sennheiser HD280 Pro: plastic fantastic, bulky, extended frequency range, loud (113 dB), 64 Ohm, long coiled cable.
What kind of amp are you looking for? For headphones I have a cheap Mackie HM-4 that can drive 4 h.p. at a barely decent level, you can buy a Behringer clone for even less.