If I buy a minecraft account do I have to pay monthly for it?

No.
You only buy the game once.

Purchasing a Minecraft "Premium" account is a one-time purchase, as it includes the Java Edition & later the Windows 10 "core edition" (which runs on the Bedrock Engine).

If you're planning on playing online with others, you could rent a server through Minecraft Realms or a 3rd party if you didn't want to set-up or manage your own server.