Easing into chess960 with start position #534
Growing into chess960 from chess1 won't happen all at once. Some players might request training wheels.
The method I've favored for the longest time is to except the rooks from randomization. If the rooks begin on the a- and h-files, the weird castling procedures won't freak them out as much.
Another way to help the newcomers — you could also consider this a kind of odds — would be to give them veto power over a number of starting positions until they see one where they feel relatively comfortable.
That idea led me to this: If a timid soul had unlimited veto power, he might reject every starting position until #534 arose — the one where the king and queen swap places but the rooks and minors begin on their usual squares.
#534 is the least unusual chess960 start, but every decision the player makes in regard to castling is altered. Castling toward the a-file takes one fewer move to accomplish, but the weak a-pawn is still a factor.
On the other wing, look at the openings that used to depend on rapid eastside castling, like the Muzio Gambit. In #518, 1. e4 e5 2. f4 exf4 3. Nf3 g5 4. Bc4 g4 5. O-O! is a deadly weapon; from #534, a different story: