if you think beats sound good then a good pair of headphones will blow your mind. you suggested buying new headphones which is why i mentioned what i personally use. you can get stereo headphones with good output which will work with laptops.
the trouble with sound quality and surround sound gaming headsets is that to keep costs reasonable individual components are of lesser quality then in a good stereo headset of the same price range. personally i would suggest going with a good stereo headset over surround gaming headset unless you play many games with the laptop with a headset. personally i dont like such headsets and use stereo headphones in such cases. your choice.
from your description it sound it sounds like you have standard 2.0 sound output like most laptops.
i'm not saying surround sound headsets sound horrible, just not as good as stereo headphones in the same price range. some may disagree and this is all opinion. pick what solution you like best.
keep in mind that many surround sound gaming headsets include an onboard sound card inside the unit which plugs into your pc via usb. this means that you do not need any special outputs on your laptop.
if you want to get a good pair of headphones i would suggest looking at studio headphones from sennheiser or audiotechnica. keep the ohm resistance low and they will be powered with a normal 3.5mm headphone jack. i believe the model i use has a 35ohm resistance and it works fine. some very expensive headphones may have a resistance of 200+ohms and these require an amplifier.
just some more information for you to consider.............