What is appropriate content when a person bears his testimony on the first Sunday and at the same time what is inappropriate?
You will not find a checklist of things you have to say, nor will you find a checklist of thing you are not allowed to say during your testimony. The simple answer is whatever the Spirit leads you to say.
There are times when discussing your family vacation is probably inappropriate, yet other times when maybe it is very appropriate. If your goal is to bear witness of a truth, and not give a travel log, then it may be appropriate.
However, the brethren have stated that testimonies should be short as opposed to long, and should state what we believe or know to be true as opposed to using the time to teach doctrine or principles.
A typical testimony is specifically centered on topics about the restored Gospel of Jesus Christ. That you know the Church is true, the Book of Mormon, Joseph Smith, or any truth learned from the restoration are typically the accepted topics you want to bear witness of. Also, the most powerful testimonies can be about a Gospel principle that you have gained an increased understanding or witness of recently.
Don’t forget to express your gratitude for the blessings you have, and your love for any one on your mind. Expression of gratitude and love are powerful ways to invite the Spirit.