The Dark Lord wanted to kill the Potters because of the prophecy.
The Dark Lord became determined to hunt down the Potters and kill them after hearing part of the prophecy and thinking Harry was going to be the boy with the power to defeat him. Snape tells Dumbledore this, that the Dark Lord believes Harry is the boy meant, and intends to kill the Potters.
“That is why – it is for that reason – he thinks it means Lily Evans!’
‘The prophecy did not refer to a woman,’ said Dumbledore. ‘It spoke of a boy born at the end of July –’
‘You know what I mean! He thinks it means her son, he is going to hunt her down – kill them all –”
- Harry Potter and the Deathly Hallows, Chapter 33 (The Prince’s Tale)
It wouldn’t be more trouble to kill the whole family than just Harry - the parents would nearly always be with the child. However, they were just collateral damage stopping him from getting to his true target. This was all to get to Harry, the one the Dark Lord thought was foretold to defeat him. He was much more cautious when trying to kill Harry than either of his parents.
“He pointed the wand very carefully into the boy’s face: he wanted to see it happen, the destruction of this one, inexplicable danger.”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
The Dark Lord didn’t particularly care about the Potter parents - though he decided against it after she put up too much resistance, he was willing to spare Lily, on Snape’s request.
“He could hear her screaming from the upper floor, trapped, but as long as she was sensible she, at least, had nothing to fear …”
- Harry Potter and the Deathly Hallows, Chapter 17 (Bathilda’s Secret)
That the Dark Lord was even willing to consider sparing her for Snape would have to mean he wasn’t particularly determined to kill her. He’d never put someone else’s wishes above his own.