basically anyone who's really easy to run into while on other business, has a loved gift that's easy to stockpile, or who fulfills a high priority objective; i.e. related to the Community Center or Year 1 Flower Dance. Or if they're strategically identical to someone who fits any of those categories (i.e. Maru has the same home and same loved item as Demetrius and their birthdays are close together, so I'll work on them at the same time).
so in Spring 1 that's Caroline, Pam, Emily, and Haley as top priority, with Clint and Linus as secondary priority (because they're on the way). Demetrius joins them once I have strawberries for him
Basically the order of friendship pursuit largely depends on when their loved gifts are "in season". But if someone's a powerful enough potential ally I'll try to force the issue early regardless.