Another good idea that might be considered is CHESKERS, which is a checker variant that combines some elements of chess. Here is a brief description of the rules:

A standard checker set is used, and the rear row of men (on each side) is replaced by (from left to right, in each player's view) a chess Bishop, a checker King, a checker King, and a "Camel" (represented by a chess Knight) which moves three spaces horizontally or vertically, followed by one space at a right angle, for example from e1 to f4. Opposing Bishops are at corners of the board's longest diagonal.

Jumping is compulsory, as in checkers, but capturing (by displacement, as in chess) with the Bishop or Camel is optional. Given a choice of jumping or making a capture, one must by made. Men reaching the last rank can promote to King, Bishop, or Camel. The object of the game is to capture the opponent's Kings