for a new person coming into this hobby on a budget, I would strongly recommend getting a pair of headphones that do not require an amplifier. Amplifiers start at $100 and really kills your budget of $200. I would stay away from headphones with high impedance that require amplification as that is just unnecessary additional spending as higher impedance does not correlate to improved sound quality. If you were going to spend $300 on a $200 headphone+$100 amp, I would tell you that you will get better overall sound spending all $300 into a nice pair of headphones.
For headphone impedance, something with an impedance between 16-32 ohms would be ideal, so you can use it connected to anything. Lower than 80 ohms with a sensitivity of 100 dB/mW should generally work without an amplifier. Basically, almost all closed portable headphones on the marketplace should fit these specs, but just something to double check. Not really specs to obsess over as these specs do not correlate with sonic performance, just want kind of other components you need in your chain.
Also, consider this: Closed headphones will give you noise isolation and generally speaking more bass response. Open headphones will sound more natural and realistic with a better sound stage. Generally, open headphones give you better overall sound quality if you do not require noise isolation or crave a bass-heavy sound signature. However, most open headphones are designed to require an amplifier.
At $200, there are many great closed headphone options.
CLOSED OPTIONS:
1) The most commonly recommended budget sub-$200 pair of headphones are the Audiotechnica ATH-M50/M50x ($120ish-$169ish, the ATH-M50x is currently available at buysonic for a discounted price of $140, but be aware that this flash sale site does not allow returns for non-defective products). V-shaped sound signature that is very popular and pleasing to listen to. The often recommended pair of headphones to newbies. Just do a quick google search and they pop up on top lists all over the place.
Some of the popular closed $200 to $300 headphones that are a few years old are now, so you can find them at discounted prices nowadays.
2) Most inexpensive: The cheapest well-reviewed closed option may be currently discontinued Logitech UE600 that was favorably compared to other $300 headphones. Since they have been discontinued, you can find them for sub-$100.
3) Most comfortable: The Sony MDR-1R can be easily found for sub-$200 nowadays, they are a lush rich mid-centric with a mid-bass boost, extremely comfortable (most comfortable pair of closed portable headphones I have tried). Replacement Sony MDR-1A model has just been released.
4) Audiophile sound: The AKG K545 can be found at sub-$200, very neutral pair of headphones with a slight bass boost as well. Great sound stage. I would consider this to be the best neutral-oriented sound quality you can get at the sub-$200 price.
Your choices: The V-Moda M80 are on-ear headphones, so they will not noise isolate as well. The Crossfade LP2 have a very significant bass-boost that does overshadow the rest of the frequency response (depends on what you are looking for if you will enjoy this). For their price point, I think there are better sonic options out there. Note I have tried both and they are not very comfortable to wear for extended listening sessions.