It depends upon the business you want to start because first, you need to describe the Budget of your small project. Some people will spend more on advertising to get awareness about the project so it depends on the projects and the advertising.
Have you ever seen where a company is about to start up a project and goes for a crowdfunding? Well, they always talk about hundreds of thousands and possibly millions of dollars. But since you said a small project, which I know, is likely to take place online, I would say make a budget of $5,000 to $10,000.
In my opinion, this much of budget is a very good amount of money and you can easily start any kind of small project with having this much of budget. The most important thing which you need to take care of before even investing your money is to think well and then decide the most profitable investment. Just do not decide the things in a hurry. You need to be very careful if you want to get something in return.