Gentlemen: Unbutton your vests ... the bottom button anyway. Most of the accepted men's style rules were established by the British royalty over 100 years ago. Of those, most were set by The Prince of Wales / Duke of Windsor. (He's the same guy.) However, the bottom button on the waistcoat (that's what Brits call a vest) being undone was taken from King Edward VII. So remember to leave your bottom vest button undone when you wear a 3-piece suit.
Of course, a 3-piece suit is pretty natty, but if you really want to have fun, go with a contrasting vest to add a little more panache.
Another important rule for vests is that they should be low enough in front to cover your waistband or belt. (See top picture.) Speaking of belts, technically, you shouldn't be wearing a belt with your vest. You should be wearing suspenders or "braces", as they are called in Britain. However, that is the most formal rule which many men do not follow. If you do follow this rule, remember that the suspenders are hidden underneath the vest. (Suspenders used to be considered underwear and weren't supposed to be seen.)
A vest that fits you well will not be too loose in the arm holes, or look baggy. If it does, then it is too big. On the other hand, if it pulls in the front and forms an X, it is too tight. As legend has it, that's what happened to King Edward VII and how leaving the bottom button undone came about. The King liked to eat. Supposedly, after a quite hearty meal, he needed to unbutton the bottom button of his vest. If royalty did it, it was a signal that the "regular guys" could do it too.
Lastly, you do not wear a tie clip with a vest. One of the vest's jobs is to hold a tie in place, so a tie clip would be redundant.