The best backup device is an external hard drive which is large enough to contain the contents of your computer. If you intend to use Apple's TimeMachine backup you should determine how much of your hard drive is being used now, estimate how that will grow over the next 12-18 months and add it to the current size. Double that number and that is the minimum size drive you should buy for your TimeMachine drive. USB is probably your best choice - since you don't have a 2012 Air don't go to the extra expense of buying a USB3.
Given the trouble you are having though I would make it a priority to copy important and irreplacable files so you might want to use that drive (or a thumb drive if that will be large enough) to copy the documents, pictures, and music folders. Then do a TimeMachine backup.
Then get the computer to an Apple repair shop or call AppleCare. There are many possible issues but a hardware fault would be near the top of my list.