I am now preparing a new faucet and I do not know which work might be better attracted to users is Litecoin or Dogecoin and is there a better job than them for users
They're both popular coins for micro transactions. I don't think there is a wrong choice.
And what's the best way to spread my faucet so fast?
You can spread the word by creating an announcement thread here on bitcointalk. You can buy banner ads on crytocurrency focused website. Depending on your budget you can also pay for some blog posts.