LOL, the trinity isn't a club. XP
Its just the three most popular jump series to American fans.(Bleach was considered part of it before it blew up in japan)
One piece, naruto and bleach.
Personally, I don't care much for naruto these days, and I don't even like bleach anymore.
My top three jump series are One piece, Hunter X Hunter, and D.Grayman.
I tried Gintama, but didn't like it too much. At least not as much as Hunter and D.grayman.(which when I started reading, I couldn't put down.)
but yea, the trinity is just a term used to refer to the 3 mangas American fans associate with Jump. It wasn't a pre-existing thing.
Edit: the reason you never see ichigo with luffy and naruto in stuff like that is because ichigo is a prick, and wouldn't fit in with them. So they said fuck him and brought goku back.
Even tho bleach is 3rd, its popularity isn't comparable to naruto and one piece. Although Bleach did pass naruto up one week, but thats because naruto started sucking…...bad. Now that Bleach is sucking and naruto is somewhat interesting, the order is probably back to normal.