In terms of getting access to the widest selection of the FF series, it is a pretty good system since PSN will allow you to purchase most of the earlier games. You'll still miss out on some of the PS2 entries and possible FFIII and IV since I believe they are PSP exclusive but whatever. I am not fond of the PS ports of V and VI for the system but it's better and more cost effective than trying to track down the GBA titles and a system to play them on.

FFXIII is a terrible game and I cannot really recommend it, while the sequels drastically improve the gameplay, they find ways to make the awful plot of the first game even worse. Still, XIII is pretty much a love it/hate it, experience so there may be a chance you would enjoy it.