Need A New Speaker System For Around $300

Go to any best buy and they should have receivers as well as blu-ray home theater combos. They will come with a 5.1 setup of speakers and sounds exactly like what you want. Surround sound, bluetooth, movies (blu-ray/dvd/), passes HDMI video through and plays its audio. Samsung, Yamaha, Pioneer, look at these brands. This will be great for gaming and movies. Since you are willing to spend 300 dollars you should end up with something on the higher end of the spectrum. These systems are surprisingly cheap for what they are.

Quick note: Keep an eye out for "hdmi passthrough" and "ARC". ARC will let your system receieve audio back from your TV assuming it supports this, meaning you won't need to use an optical cable for getting audio from devices connected to the TV/smart TV apps. HDMI passthrough will let you use one or more devices through your receiver/combo which can send it's uncompressed 5.1 audio to the speakers and the video to the TV.

example: http/www.bestbuy.com/site/samsung-4-series-500w-5-1-ch-3d-smart-blu-ray-home-theater-system-black/3188027.p?skuId=3188027

another example (on clearance atm): http/www.bestbuy.com/site/samsung-6-series-1000w-5-1-ch-3d-smart-blu-ray-home-theater-system-black/4832115.p?skuId=4832115

Also, portability/taking speaker with you isn't really an option. Considering your 300 dollar price range you should know that a good Bluetooth speaker for your phone can be found pretty much anywhere for cheap. However, surround sound isn't something that can be done with a portable device.