Yes. Mayroon is the proper word to say, spell and write.
Meron is a slang and not included in the filipino dictionary. This is commonly used by people who are talking, texting etc. but should not be used in proper writing.
Anyway, in your example,
Mayroon akong ng kotsche. and Meron akong ng kotsche. (It should be Mayroon akong kotse. Meron akong kotse)
Hope that helps!