ESRB has listed GTA 1 and 2 for PSN.
It looks like Grand Theft Auto 1 and 2 will be heading to the PSN by the way of PS1 classics. Which means you will be able to play these games on the PS Vita and PSP.
The listing also shows the three PlayStation platforms. With the addition of these games on the service, the network will have all GTA games and if you are new to the series, it’s not a bad way to get accustomed to it by playing all these games.
GTA 5 comes out on September 17 so there’s enough time for you to play these games if you haven’t already. The listing can be found on the ESRB site via search.