FG content is definitely harder than vanilla content, so IMO it depends on your tolerance for pain 
Let me preface this by saying that Iâm a pretty casual player. Others are gonna tell you âeverything is trivial up to ultimate regardlessâ, but you can decide for yourself Also, I was playing on Veteran with a new character but Iâm not new to the game; have a shared stash packed with blues and purples.
I started a new Shieldbreaker and went to FG right after Act I. It was fine for a while but boss packs and challenge dungeons started getting tough. When I got to the last area (lava zone), I was level 30ish but I had three deaths in a row so I decided to go back to vanilla Act II for a while and return later. Breezed through everything in Act II including Steps of Torment, even though all the enemies level to you in both FG and Vanilla now (based on what devs said pre-release I believe everything everywhere scales all the way up now, but I canât confirm that yet).
So, itâs your call but thereâs no problem moving back and forth between acts. To Paavo about quests: itâs possible some sidequests in FG wonât open up till you finish the vanilla story, but you can definitely get through the main FG questline right after Act I; there might be some more stuff you need to go back for later, donât know. Iâm kinda wondering what will happen with Deathâs Vigil/Kymonâs Chosen in Act III, due to ⌠some stuff in FG I wonât mention because spoilers
Another consideration: you donât get any new pack tabs in FG, so you might want to pick up the first two before you go in just to avoid endless trips to town
TLDR: you can go in right away but FG is harder, and you can also pingpong back and forth between FG and vanilla with no issues.