What are new players supposed to do now?

Anniversary chains should be out for a while, I think until Nov. 2026. They all target characters that you naturally attain via getting to level 85. I wouldn't worry so much about catching up as just playing the game. 

I didn’t use any of the Era Characters to complete the anniversary quests, they all used Legacy Characters - characters you get without participating in any era game mode. I’d suggest finding a guild/allies so you can use their characters to help you complete the quests more quickly. Swgoh.gg also has a data base you can use. For instance, if a quest is to apply “ability block” a certain number of times, and you’re not sure what characters do that, you can google “ability block characters swgoh.gg” click on the search result from the website, and get a list of characters who can apply that specific debuff. You can send me a friend request, I have some characters you might be able to use as allies that could help. Ally code below, hope this helps. 563-553-593

From: Title Update and 10-Year Anniversary Announcement Post | EA Forums - 12879024

"Marquee characters’ shards will be farmable on a node approximately 13 weeks after their marquee event."

Marquee toons will be farmable some time after their marquee event, just like every marquee character before, since the game launched.