To be honest, I don't know enough about standalone mics to confidently recommend one for you. I have heard surprisingly good things about this guy:
http://www.canadacomputers.com/product_info.php?cPath=35_920_921&item_id=040717 and if you can afford it/like the idea of a real microphone, this one:
http://www.newegg.com/Product/Product.aspx?Item=N82E16882329005 Though, if you are just casually YouTubing, you probably don't need something that belongs in a recording studio. So here what everyone seems to think is the best mic you can add to a good pair of headphones:
http://www.amazon.com/Zalman-Zm-Mic1-Sensitivity-Headphone-Microphone/dp/B00029MTMQ/ref=sr_1_6?s=electronics&ie=UTF8&qid=1341983408&sr=1-6&keywords=desktop+mic You just clip it onto the good headset that you will have to buy and then you have high quality studio headset+mic.
As for headsets, look for something from Sennheiser or Audio Technica (The best is the ATH-M50x). if you want ultra-quality headsets without an integrated mic. Astro, Plantronics, Logitech, Sennheiser, and Audio Technica all make some of the best headsets with integrated mics.
The Audio Technica headsets I referenced are these http://www.audio-technica.com/cms/headphones/97d660ada89c32c8/index.html. I checked their compatibility with xbox 360, and I am sad to say that they only work on PS4, PC, and some mobile devices, not the xbox.
The $300 price tag might be out of your range.
You can pretty much pick anything for >$100 from this page:
http://www.audio-technica.com/cgi-bin/product_search/headphones/headphones_cat.pl?select_multiple_3=Over-Ear and be very satisfied. Many have recommended something from the ATH-m50x family. m40s would sound amazing also and be closer to your price range.
So to summarize, I think you should consider getting a set of m50s(or 40s) from Audio Technica and then buy a zalman mic to clip to them when you want to chat/record. If you want one headset with it all in it, then go for something I recommended before like Astros. I would avoid Razer and yes, even the beloved Turtle Beach, as both of those brands are rather cheap in their manufacturing process.
I hope you find something you like