Looking for a cheap gaming desk for a carpeted room

I'm finally building my first gaming PC! I've never been able to play all the games I own on steam because I went from an integrated graphics card to a Macbook.

Anyway, I got a monitor for free because my boyfriend's mom's office or whatever was getting rid of them. Sweet! But it doesn't fit on my desk, which is a small bookshelf/desk combo. Plus the chair is super bad for gaming for extended periods and there's no space to put the actual computer case.

I have a small length of wall across from my bed that I think would fit a small desk pretty well! But I don't know what kind of cheap (preferably <$100) desk I could get that has room for keyboard/desktop/mouse and space for the case underneath somewhere that would ALSO fit on carpet without wobbling.

Advice or suggestions? Maybe something like this? Sorry if this is a really stupid question, I just wanted some quality input before I bit the bullet and spent even MORE money :')