I have three toilets in my house but this only affects the one in the basement. Whenever I flush the toilet, that is, immediately after I press the flush handle, I hear a loud "thump." The toilet flushes and fills with water normally. It makes no difference whether it's cold or warm. Any ideas?

What is your water pressure, in psi?

I have no friggin' clue! I do have city water and it's not from a well. Does that help?

You could have a bad fill valve that is acting up but I can't tell without hearing myself. A new Fluidmaster 400A would be less than $10 and may fix the issue. If you decide to live with it I doubt there will be any negative side effects.

The thump is before the actual flush and fill cycle?

No, it's immediately after I push the flush handle. I've been told that I need to bleed the system of air, but I'm not sure how that's done.

There is no such thing as air in a water supply line. Any air in the line is pushed out as soon as you open the faucet the first time.

Sounds like you have a loose washer in the stop valve underneath the toilet tank or trash caught in the valve.