installing iphone OS6 from non-linked (non-synched) computer

After careful review, I would like to run the current version of OS6 on my iPhone 4.

My MacbookPro laptop at home- the one, single computer that Apple allows you to sych to- is old and will not allow me to update my iphone because it will not run the later version of iTunes needed to upgrade the phone. (I'm not going to purchase a new OS for that laptop right this second because it is 5 years old, and I don't even know if it will accept a new OS. I can't afford a new laptop just yet.) I feel like Apple is holding the new phone OS hostage to me because I  can't afford new everything all at once to get up to date to use  the installer via iTunes.

Therefore, I am trying to upgrade my phone from my work computer. It will proceed as far as I can tell, but gives me a warning stating that my phone was not backed up and none of my content or apps were saved (including ones I paid for.) I had a feeling this might happen, so I DID back the phone up to iTunes on my home laptop.

A) Is there ANY WAY to allow my phone to completely back up onto my work (non-synchable) computer and not delete everything on the phone??

or B) More scary- Will I be able to recover my old apps and data from home and re-install it on my iphone without issue after this software update?

I don't know if, once the new OS6 is on my phone, Apple will stupidly link the phone with the computer used to update it, rendering all my saved data from home useless.

It really shouldn't be this difficult for consumers to upgrade when the new OS is dangled for older devices.