My suggestion is, without making it more complicated, make sure that each game has at least one or two non-standard pieces. The reason is that if players have all standard pieces, it would still be too similar to chess (or one of the combinations of chess960).
If the game is played slow and parties are remote, games might still be analyzed by an engine. But requiring a few variant chess pieces will make the game so it is unaffected by computers - "untouched by artificial intelligence". That category of games are my favorite ones to play.
Also (for later, if you feel ambitious) try to make a theme (like a game based on some period in history or a fantasy book), and maybe even make a custom-shaped board.
Btw, I've noticed the idea of Pokeman-chess has become really popular. A lot of people are talking about the pieces, but no game has come from it yet.
I wanted to make a chess variant where you could choose the minor and major pieces in your army, to allow for many different army possibilities. I tried to keep the values of the minor pieces at about 3-ish pawns like the Bishop and Knight, then major pieces at 5-6, like the Rook, and then a Queen type piece at 9-ish pawns. Let me know how I can better balance these pieces, or other piece ideas!
Rules:
Normal pawn rules
No Castling, unless there are rooks starting on the a/h files (like orthodox chess)
Pawns can promote to any piece that is or was on the board during the current game
Before the game starts, the players choose their teams. Black chooses one queen, then white, then black chooses one pair of major pieces, then white, then black chooses one pair of minor pieces, then white, then black chooses the second pair of minor pieces, then white (the second choice of minor piece cannot be the same as the first). Players can choose the same pieces.
Players then choose the arrangement of their pieces. The King is always on E-File and the Queen is always on D-File, like orthodox chess. Also, the orientation must be symmetrical (A1/A8 and H1/H8 files must have the same pieces, same with B1/B8 and G1/G8, C1/C8 and F1/F8). White puts down their first pair of pieces (major or minor) first, then black does the same, and then white, black, white, black. Then the King, Queen, and pawns are put in place, and the game is ready to start with white's first move.
The Pieces:
Basic pieces to compound from:
Ferz (one space diagonal)
Wazir (one space orthogonal)
Alfil (Leap two space diagonal)
Dabbaba (Leap two space orthogonal)
Alibaba = Alfil + Dabbaba
Knights, Bishops, and Rooks
Minor Piece (Choose 2):
Knight
Bishop
Guard (Wazir + Ferz, moves like a king)
Hunter (Wazir + Alfil)
Warrior (Wazir + Dabbaba)
Scholar (Ferz + Alibaba, but no leaping: basically can move diagonally in any direction by two spaces)
Major Piece (Choose 1):
Rook
Paladin (Knight + Guard)
Sage (Bishop + Dabbaba)
Nightrider (Knight that can keep leaping in the same direction)
Queens (Choose 1):
Queen
Princess (Nightrider + Bishop)
Empress (Knight + Rook)
Duchess (Knight + Alibaba + Guard)
There are 240 different armies possible and 1440 different starting positions, not to mention all the different matchups. Also, I tried to find commonly-used names for the more common fairy pieces, but I ended up making up names that I thought worked thematically/sounded cool for a lot of them.