Safari Update

The last version of Safari for OS X 10.8.x was Safari 6.2.8

If you can't or don't want to update your OS X to a more current version, another option would be to download and install Firefox and use that instead of Safari. https://www.mozilla.org/en-US/firefox/desktop/

Read Upgrade to OS X El Capitan - Apple Support.

Assuming that you are already in the habit of routinely backing up your system you can evaluate El Capitan at no risk and at no cost. If you do not routinely back up your system, you should. Obtain an external USB, FireWire, or Thunderbolt hard disk drive for your Mac, then download and install El Capitan on it. You can choose to start your Mac from that disk or the internal one using Startup Manager (hold an option key while you start your Mac), and evaluate El Capitan at no risk whatsoever to your existing installation. Just be sure to designate the proper installation location for El Capitan when you get to that installation step.

Running OS X from an external USB hard disk won't be as fast as the Mac's internal one, but it will be sufficient to draw conclusions regarding its suitability for your needs.

An external hard disk drive of adequate capacity can be purchased for well under $100 - much less than the cost of some previous OS X upgrades themselves. When you satisfy yourself that El Capitan works for you, then "clone" the external disk's contents to your internal one, and use the external disk for backup purposes — which you ought to be doing anyway.

I've read many bad reviews about the later versions.

One month after it was released there were approximately 20 million El Capitan users worldwide, and 99.98% of them hadn't posted any reviews on the App Store. This support site is primarily intended for those experiencing trouble of one sort or another, and the vast majority of those problems are due to incompatible, outdated, or ill-conceived products that should never be installed on any Mac. They exist in same proportion as every other OS X upgrade there has ever been, since Jaguar at least.

There is no reason to rush into any OS X upgrade, but you are using a version whose last update was over two years ago. Eventually you're going to experience more of the same problems you described. You can use Firefox for now, but just be aware that eventually it too won't work, and by that time El Capitan may no longer be available either.