When considering the touch move rule, I am still unclear about the legal sequence for a capture. Example, white intends to capture a took on a8 with rook on a1 (open file). Does white have to touch black's rook first? The way I read the rule, if white touches a1 first, they can only play a2 through a7, since touching a8 AFTER a1 violates the rule. What is the legal sequence?
Here is what the FIDE Laws of Chess have to say:
4.3 Except as provided in Article 4.2, if the player having the move touches on the chessboard,with the intention of moving or capturing:
4.3.1 one or more of his own pieces, he must move the first piece touched that can be moved
4.3.2 one or more of his opponent’s pieces, he must capture the first piece touched that can be captured
4.3.3 one or more pieces of each colour, he must capture the first touched opponent’s piece with his first touched piece or, if this is illegal, move or capture the first piece touched that can be moved or captured. If it is unclear whether the player’s own piece or his opponent’s was touched first, the player’s own piece shall be considered to have been touched before his opponent’s.
So, if the first two pieces you touch are one of your pieces and one of your opponent's pieces then you must capture your opponent's touched piece with your touched piece. Order is irrelevant in this case.
If you first touch your piece and then one of your opponent's pieces which you cannot capture with your touched piece then you must move your piece even if you can capture your opponent's touched piece with one of your untouched pieces.
If you first touch one of your opponent's pieces and then one of your pieces but can't capture the opponent's touched piece with your touched piece then you must capture your opponent's touched piece if you can. Otherwise you have to move your touched piece.
Overriding these rules is the rule preventing you from making an illegal move. You may only move a touched piece or take an opponent's touched piece if that move is legal.