Does the spanish word linda mean nice or would it mean more something like beautiful/pretty?
Pretty, more often than not. It can mean 'nice' in the sense of 'fine' or 'lovely'. If you mean nice like a nice person I'd normally say simpático/a.
nice person=amigable (friendly), agradable (nice), simpático (nice), amiable (amiable, affable)
Usted es muy linda mi cielo. You wouldn't use usted in this sentence and then finish it off with "mi cielo" as when you address someone likewise you are very familiar with them i.e. Mi cielo can mean my heaven or words to that effect come to think you wouldn't say es you would say eres muy linda.
It all depends on context. When I used to play in a band with South American guys it could be to describe a tune, an arrangement, a solo. At the same time it could be a lovely girl, a beautiful guitar...
It's flexible but there is always the suggestion of beauty of something special.