Jackett comes preloaded with 574 indexers, and none of the ones I use are private. All of mine are public indexers, you just have to know the names of some popular torrent sites. I discovered half the indexers I use from people on r/Piracy (before the migration) talking about how much they like how they work. That’s how I found Idope, Knaben, and Torlock. Others, like 1337x, Nyaa.si, LimeTorrents, and EZTV are all indexers I was familiar with as I had used them personally and recognized them when I clicked into the “add indexers” drop-down on the interface. Barring all that, you could just ask someone else to send you a screenshot of all the indexers they use on their Jackett setup. Here’s a list of the ones I use. Adding indexers to Jackett is basically the easiest part, and you only have to do it once.
I’m not sure if they have an android version of Jackett. It would be a dream come true if that were the case, but I’m sure it would be listed in the Jackett github page if a mobile version was available. Sadly, there’s no mention of anything like that on the github page.
Really glad to hear you were able to get Jackett working, though! It really is an amazing program.