I have a test site that has been using windows-1252 all along. They do need/use some symbols like the square root symbol. And they have no need to display in another langu
Windows 1252 is one of the many many fixed size character sets. Mac has its own set. there are a few ISO for various parts of the Europe and for some other parts of the world. Most of them have slight variations.
The good point is that you have a fixed-size character, meaning 1 character = 1 byte no matter what.
The bad points are:
That include any citation you would like to make. In windows-1252 you can't display russian, greek, polish ...
UTF-8 is the standard encoding for unicode representation on 1+ bytes. It can represent a very large majority of the characters you may encounter, although it is designed for latin-based languages, as other languages take more storage space.
It in used in XML, JSON, and most types of web services you may find. It is a good default when you don't know what encoding to use. It allows to limit the number of encoding issues, such as "I though you were in Latin-1 / No, I was using latin-9, but then this guy on mac used Roman". If you have more than 1 people working on the content of the website, they may have different encodings on their plateforme, and therefore your content may be messed up at some point.
UTF-8 is, as far as I know, the only way to easily standardize the encoding used between people without discussion.
Typical example is, if your website is encoded in windows1252, and the new dev has a mac, you'll probably be in trouble.