As Sath noted, there are some ways you can progress. I would recommend blowing all your AP to do the story missions since we have 1/2 AP now. Early on, you should be able to do them without any refills at all. Once you're rank 30, 50, a lot of other stuff will open up. Not to mention you'll have enough to do one or two more 10-pulls during the SSR bonus rates at the end of the month.
But it's important to note that at the end of the day, this is a grindy game. That part won't change. You'll just be grinding on the next tier of stuff.
In terms of value, start-dash and surprise tickets are going to be much better value. But if you're just looking within the phases of the star pulls, IMO the one tomorrow (dagger / harp) is better than today's (H2H / katana). The Katana characters are quite good, but most of the H2H characters are only mediocre, so only half are good. But for tomorrow, at least 6 or 7 out of 10 are pretty good (some very good).
https://pbs.twimg.com/media/Cf_tUoOUsAAoJB5.jpg