Is there an advantage to applying for smaller, not as well-known scholarships?

There is no wrong way to apply! The more you apply the better!

There is no wrong way to apply for a scholarship! If it's smaller and less well-known, then there will likely be less applicants and your chances of receiving it will be higher. Every year during college I always applied for my local community center scholarship that didn't give out much financially, but it was always enough to pay for my textbooks, and that was so helpful! However, the bigger ones usually have more money to offer and more recipients to give the money to. It all depends what you are willing to put the time and effort into applying for, the more the better, but they do take time so be wise in which ones you choose.