If I Married A Man With A Suffix On His Last Name (xxx, Jr.), Do I Take It When Changing My Name?

No because he was name after his Dad you would only take his last name not Jr

Yes of course because the Jr separates him from the other party or his father from him and his name, it should be used at all times when handling business especially good luck

Hmm...good question, and both of the previous answers are good responses. Here's yet another answer for you.....My husband is latin. 9 and a 1/2 out of 10 latin boys are named after their father. But they do not use any type of suffix to distinguish Jr. Or Sr.  And their names go on for generations, i.e., Great grandpa is (exp.)Luis Rios...grandpa is Luis Rios, father is Luis Rios, son is Luis Rios and so on. However, they do also keep the mothers surname, that is why there is no need for the Jr. & Sr.  But...me for instance....my husbands name is passed down for generations, but as I said, each generation has their mother's name included in their name, but I do not use his full name, just his name (from his father's side.  Phew....I hope I didn't confuse you.  

A wife who uses the title Mrs.
would also use her husband's full name, including the suffix. In less
formal situations, the suffix may be omitted. Hence: Mrs. Lon Chaney
Jr. On a wedding invitation, but Mrs. L. Chaney or simply Shannon
Chaney for a friendly note. Widows are entitled to retain their late
husband's full names and suffixes but divorcees may not continue to
style themselves with a former husband's full name and suffix, even if
they retain the surname. (per wickipedia)

I think it does become part of your name when you are referred to as MRS----.  You are Mrs. John Smith, Jr.  You are not Mary Smith, Jr. Lol
If there were three John Smiths in your town ( John, John Sr. And John Jr), how would anyone know which Mrs. Smith was which, anytime the name was written.  I could be wrong but it is the only way that makes any sense to me.

The Jr., Sr., III etc are official parts of his given, legal name.

No you would not , that is a name only to him