Does It Cost Money To Run A Personal Minecraft Server?
Short answer: No, It won't matter what you do.
However, how you spend the money and the total cost can vary depending on what you need. If you want the server to run close to 24/7 and you dont want to use your pc there are generally two options available to you.
You can rent a server from a server host for a few bucks per monthly to 10 to 15 dollars per month, depending on what you need. This is the cheapest option, but it will end up costing you more long-term.
You can purchase a small, like a raspberry pi, with additional hardware modules and set this up yourself. This will cost you around 80 - 100 bucks at the start, and you have to manually set it all up. You should not be charged any additional fees after that. (Hardware can break, but let's ignore that for now.
Now, if you want to keep running it from your PC you could invest in a wired connection to stabilize connection and reduce lag. This will cost you the price for cables and some time to set it up.