Traditionally, wedding invitations are addressed in cursive by hand. This is THE proper way to do it. If you can't write cursive, printed letters are acceptable. Some brides hire people to address their envelopes (calligraphers). This is expensive and unnecessary.
You don't care? Fine, but you need to know the rules before you decide to break them. Some brides run their envelopes through their computer printer. Tracing the letters with a pen is sometimes done. Please don't use sticky labels! Those are strictly for junk mail.
These are typical forms of address. Do not use abbreviations such as "St." for Street. The post office prefers that we use standard abbreviations for the USA states, so I bow to them.
Married couples: Mr. and Mrs. John Smith, or Ms. Jane Smith and Mr. John Smith, or Doctor Jane Jones and Mr. John Smith
Unmarried couples: Ms. Jane Jones
Mr. John Smith (on separate lines)
The title "Miss" means unmarried woman of any age. Many ladies prefer Ms.
Divorced woman: Mrs. Jane Jones or Ms, Jane Jones.
Widow: Mrs. John Smith (unless you know she prefers something else.)
Same sex couples are addressed in the same way as any others. I would suggest alphabetical to determine who is listed first.:
Mr James Jones and Mr. Robert Smith (married) (Female couples may both use the title Mrs. if they prefer.)
Ms. Jane Jones
Ms. Sally Smith (unmarried)
For plus ones, I would try and find out the actual name and write it on the envelope, but otherwise, I suggest inserting a note that says "You are invited to bring a guest."
The inner envelope is an old tradition. In the old days, the servant would remove the dirty outer envelope when it arrives, and present the inner envelope on a silver tray for the lady of the house to respond. (Shades of Downton Abbey!)
The inner envelope contains the names of everyone who is invited along with the couple:
Mr. and Mrs. Smith
(Miss) Susan Smith
(Master) Robert Smith
(No address is written on the inner envelope.)
If there is no inner envelope, you can write this on the outer envelope. It is OK to write the children's names on one line together below their parent's names. Never write "The Smith Family"! They might bring Grandma and Uncle Ed! If there are simply too many in the family, and no inner envelope, I would put a note in to clarify that the children are invited.
NEVER, EVER WRITE "NO CHILDREN"! If you don't want children, then don't write their names on the invitation. If there is a misunderstanding, you will need to make a telephone call and say, "I'm sorry, but we didn't mean to invite the children."