That is a laptop. You are not going to easily upgrade the HD without some basic tech skills. You would have to buy a HD and likely a seperate imaging software and a cable. Or you can just use an external HD. In which case you can get any USB disk. I recommend USB 3 (avoid usb 2 due to speed).
Another alternative is to take it to a shop and pay them to upgrade the disk (swap your internal out for a new one). Their service fee will be close to your requested budget, and so might not be a practical choice for you.
Finally any SSD worth owning AND larger than 256gb is going to be over budget. You would be disappointed in the performance drop if you went from a SSD to a HD. For an external connected via a USB cable, you can get away with a HD.
Recommended HD:
I don't like this unit, but it is in budget
https
/www.amazon.com/Toshiba-Canvio-Basics-Portable-Drive/dp/B00N2S6ZUQ/
Recommended replacement SSD:
https
/www.amazon.com/Samsung-2-5-Inch-Internal-MZ-75E1T0B-AM/dp/B00OBRFFAS/
There are 500gb (might be a tight fit, depending on your applications, photos, etc) or a roomier 1tb. Neither are on budget.