How much free space do I need to install Mavericks 10.9.4?
You have more than enough space on your disk

I'd very much like to see a picture of your 'About this Mac screen', from the  Apple menu, just to be certain you're heading in the right direction.

It should look something like this…



Also, you'd be better off installing the 10.9.5 Combo Update which will install all updates from 10.9.0 to 10.9.5 without needing any intermediate steps.

After comments &amp; posted picture:
You cannot jump over an update using just the delta update, only using a combo.