Some common recommendations. FYI, I haven't heard most of these headphones, I'm just regurgitating things I've read as I've made my own headphone choices. I've had the experience of nobody responding to my recommendation posts before, and it sucks, so hopefully others can chime in too...
In general, at least in my opinion, metal sounds bad with a large soundstage (everything sounds too far away, not in your face and aggressive) and classical sounds bad with a small soundstage (not enough sense of grandeur and scale). So you're probably going to need to pick one over the other.
Beyerdynamic DT990 250 ohm is one that I have owned, and it does both genres decently. The soundstage is large enough for classical, but the base and treble are aggressive enough to make metal sound exciting. The DT770 is very similar, but closed. They can be driven acceptably from a laptop, but I couldn't get enough volume from an ipod.
Grado is commonly recommended for metal, as they are fast and energetic. Don't require an amp either. The SR225 is considered the sweet spot of the line, and they are around $200. The downside is that they have a smallish soundstage, which many people find unappealing for classical.
Audio Technica M50 are often recommended for unamped headphones in your price range. Some people also like the AD900, which have a bigger soundstage.
You also want to look at Hifiman HE-300. I really love the HE-400 (which to be fair, uses a completely different type of driver technology), but the HE-300 are Hifiman's cheapest headphone and have been getting some good review.