I would say continue to use the green screen except instead of green screening an image or landscape, for ex. the money background you used, or a landscape such as a fake street, etc. Instead of using one of those (because, often times, it comes out looking fake & green screened) just use a white layer. Simple. It can't look shitty because it's just white. It's almost like putting up a white sheet, but better because it leaves no shadows, no discoloring. It makes it look more professional for many reasons, one being - it looks less generic. Your money background looks fake, generic, green screened, like anyone can do it. What is the purpose of green screen? TO make something look BETTER. What is the purpose of using green screen when your making the video/background look worse? Nothing. To many people get green screen happy & think that as long as they're using one, it's better or more professional, but it's not the green screen that is professional, it's what you can do WITH the green screen. It's purpose is to make things look sharper, in a realistic tone.
When thinking how can a white background look better, think of this: A commercial advertising a medication, for heart burn, dieting, doesn't matter. Think about the background a lot of those commercials use, BASIC - WHITE - BACKGROUND. Nothing in the background... except happy images floating by. Use that same theory commercials use, they're making hundreds of millions of dollars using a white background, it works lol. I take filming courses for school, been doing it since I was before I was a teenager, just trying to help.