Advice Needed: How to upgrade iPhone 4S OS 5.1 to v6 or v7

I have an iPhone 4S/16GB running OS 5.1.1 and would like to upgrade to at least 0S 6.1., or v 7.1 if that's more bug free and as fast running as 6. I put off upgrading the OS previously because I assumed that the phone would run faster on an older OS. Now some of my apps won't run unless the OS is at least v6 so its time to upgrade. The problem is that now after trying every possible way I can find online, I just get error messages (3194, 11, 4016) and can't upgrade/recover my OS to v6.1.3 or v7.1.2. I've used Tiny Umbrella to try and solve verification problems, but all without success. It seems I don't have the necessary shsh 'blobs' to allow the upgrade ??

Could someone advise as to the best path forward? The phone is legal, unbroken but I'm open to running the jailbreaK routine if that will solve my OS upgrade issue. Any advice with resource links will be appreciated !!