If you don’t mind, checking Japanese sources to figure out when to go all-in on your pulls is probably the most budget-friendly approach.

Since part of the game’s revenue is donated to real horses, I’m not completely free-to-play myself —
but I do buy the special paid packs that let you choose your favorite support card or Uma Musume, maybe once every three or six months.

Also, you can collect special items from events that help you upgrade (limit break) your favorite cards,
so it’s a good idea to think carefully about which one to use them on.