tldr: he used a basilisk because that was the best option available to him
This answer is based on the assumption that all the information we have about Slytherin are correct. I also recommend you to read and upvote this as it's a good answer. But I also think it's just a theory, and as more new material gets added to the Harry Potter universe, I think we will be able to come up with more and more fan explanations to fill up plot holes in the main books, regardless of whether they might be correct or not. Also, the books don't imply that any thing the readers get to find out about Slytherin are false, so this answer is based on, as Prof. Binns put it,
...solid, believable, verifiable fact!"
Prof. Binns says that
"Slytherin, according to the legend, sealed the Chamber of Secrets so
that none would be able to open it until his own true heir arrived at
the school. The heir alone would be able to unseal the Chamber of
Secrets, unleash the horror within, and use it to purge the school of
all who were unworthy to study magic."
He also goes on to say
"That is believed to be some sort of monster, which the Heir of
Slytherin alone can control," said Professor Binns in his dry, reedy
So he needed something that
- could be used as a weapon to get rid of people unworthy to study magic
- could be controlled by his true heir
- could be stored without being detected while he is not around
Given all these conditions, the basilisk is the perfect weapon for him, as
- it turned out it survived for more than 1000 years, staying dormant until called out
- it could travel through the castle undetected
- it did everything it was told to by his true heir
Also, if we are to believe Voldemort inherited his narcissism from his great great...grandfather, then a magical giant snake is a perfect thing to be placed there, as it was the symbol of his house, as well as the thing he was famous for being able to talk with. Voldemort is shown to put a lot of importance on symbolism that exemplifies his greatness, and his link to magic and Slytherin. Perhaps this trait comes to him from Slytherin himself, in which case it is more logical that Slytherin would decide to place a snake there.
Also, as @TheAsh has pointed out at other places, "get rid of people unworthy to study magic" may or may not mean killing muggle born students at the school. But whatever that implies, he needed to hide something dangerous in the chamber, which would also be subservient to his heir. As the events in the book showed, the basilisk was perfect for this.