If you plan to spend money then choose monthly to open new account so you will be eligible for the limited characters special ticket.
If you are just F2P anytime is fine.

I'm grinding for class weapon to unlock Tier 4 jobs too. The grind is real man...    But no better time to do it than now with magnafest on. 

I used Qooapp to install the app, but some just play from mobile browser.
I think you've missed the best time to start by a week or so.    Normally at the end of the month/beginning of new month, they have legfest where rates of drawing SSR characters are doubled. That's the best time to reroll, less painful that way. For F2P rerolling will be even more crucial I think.

There's this one character that some considered OP, Summer Zoeey. She's not always available but in the last legfest in early May she was in the draw pool.