This is gonna sound crazy, but you can grab a pair of Koss Porta Pro for $50. It's considered by most to be the gateway drug to hifi. It's got a warm sound signature. The sound stage isn't super wide, but I've found the thing to be amazing for gaming. It's light so you can wear it for hours. The mic is awesome (don't buy the KTC version). You won't find any bad reviews of these headphones.
Also, if your goal is to have start delving into a higher quality sound, my recommendation is not to go wireless, since Bluetooth compresses audio. You don't want that if you're paying upwards of $300 dollars. Get a good pair of light, wired headphones.
If if you don't get the Porta Pro, my other choice is B&O H6. It's awesome! I got mine for $169 in amazon for the 2nd gen. They're usually $299. The 1st gen is really good too. The only difference is 1st gen has a punchier mid. The first gens are cheap. The way to tell is 1st gen has green inside the ear cup.