In your profile page/ tab you will see "following", that's where you can see you you're following and also your followers in that tab. Separately at the top (mobile app), you'll see a star and a "bookmark" icon, that's where you'll see your favorites and bookmarked toots.
And as for fun accounts, check out the tweet below that has a bunch that can get you started and fill your timeline slowly. Also keep in mind, you can follow hashtags.
https://toot.cat/@Hashtags/110742042033681800
As for searching, the new mastodon 4.2 I think brings in autocomplete for searches, so you'll see that implemented soon on mastodon servers.
Hope that helps initially!