yashiharu:
should i go for a relay module (24v 10A)?
it seems easier & better, even for future study ...
Ahhh rats what you asked just reminded me that what I wrote was -NOT- exactly straightforward-correct. I said 'two shields' because for a newbie Arduino is meant to be as plug-n-play as possible. But, you can't -simply- stack two motor shields. You'd need to bend out the address pins of the -top- shield, and patch those pin over to other address pins on the main board.
Relay board, sure , that's 100% appropriate too. Solid state such as the 298 is faster and quieter. For a pump, speed is not an issue. You don't need to go as far as 10A though, 100% headroom is perfectly OK.