The word order is not very different, as like English it is spoken basically Subject-Verb-Object. Sometimes at the start of a new sentence or phrase a short form verb like sam or ćeš will follow, but this is because they are in the short form.

Word order is very flexible, like in Russian but it isn't quite as, because enclitics (words like li, se, and genitive and dative enclitics like me and mi) have a strict order in the sentence, but you don't need to worry about that right now, I think.

Both "mio sam" and "jesam mio" are correct, although I'm not sure if you are saying what you want to say, as it means something like "I am dear/sweet". I'm a Croatian speaker though and we don't really use that word so often, but I don't think it would be any different in Serbian.

And the name should end with vić.