We need some more info to give a better answer such as what kind of website is being hosted, does the website have lots of images or videos etc?
But for a simple wordpress website you should be able to handle at least 20,000 to 60,000 unique website visitors to your website with 1 GB of ram on a VPS server.
Some shared hosting has hosted websites just fine getting 10,000 to 20,000 unique visitors per day but they would be a quality web host.
Your limit to the amount of visitors will depend on how the users are using your website and the ram and CPU will be more of your limit than anything else.
You can always increase your Ram on your VPS server if needed as traffic grows for your website.
Either way if you're getting 10,000 to 20,000 unique visitors per day to your website you can likely earn some good money and be able to afford a good quality dedicated or VPS server.
There's also the option of cloud hosting where you easily scale up the resources as your website traffic grows overtime.