I'm in the same boat, and I don't have a PC to play any of the other games aside from CS1/2 (which I played on PS4) either. I opted for this: I'm watching plot summaries on YouTube. There are some really good ones out there, that do amount to quite a few hours in and of itself, and whilst of course it isn't as emotional as playing the games myself, I am now familiar with Skies' characters and their stories, and am currently in the process of learning about the Crossbell story. I am a busy woman, so even if I HAD a pc to do this with, I am not sure I would.
It's really up to you though. I won't deny though that I considered the factor that the sales of CS3 may determine whether or not they bring over CS4, and if everyone just waits for the Crossbell games or starts with the Sky games (as, in my perception, a lot of people have only really gained interest in the series after CS3's announcement, most likely due to the more appealing graphics as well as the fact that NISA is actually marketing it), ne therefore only buys CS3 in like a year when it might be on discount... That may or may not keep us from ever getting CS4 over here. And whilst I know nothing about the story contents of CS3/4 aside from what the CS3 demo showed, I have been told that you would not want to play CS3 and then stop there. So... Yeah.