You can't use that software to install the new one. You'll have to download a new client. Since you played 1.0 before (amount of time doesn't matter, though you are right about the 3-month requirement for Legacy status), you will get a 14-day trial before you have to start subscribing. You do not have to purchase ARR, though, unless you want to or unless you want the 30-day trial.
At the very least, this is how I understand it. I'm a Legacy member, so I'm a little different, but I believe this is how it is.
Here's where you go to download the Windows client: http://www.finalfantasyxiv.com/playersdownload/na/
The client file is 109MB, which, when run, will download the game for you.
Edit #1: addition of stuff in parenthesis
Edit #2: addition of link to Windows client
Edited, Mar 7th 2014 9:37am by Vaaniks
Edited, Mar 7th 2014 9:46am by Vaaniks
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Primary World: Hyperion
Free Company: Jormungandr
Legacy Member
Main Character: Fialas Dawnren: Level 60 BRD/AST/MNK/DoL, Level 16-50 On Everything Else