THE cigar and the glass of champagne add that tycoon touch to the youngest-ever pop star to join the millionaire set.    But it is all very new to the 18-year-old Herman of the Hermits, as you can see from the way he is holding that cigar. Not to mention the school blazer he is wearing.     Yesterday a Metro-Goldwyn_Mayer film contract that will bring Herman and his four Hermits a cool £1,650,000 over the next five years was announced in London.     One of the planned films is a remake of the Marx Brothers' comedy classic, "A Day At the Races."     Herman, who starts a six-week tour of America next week, will be credited in the film titles under his real name - Peter Noone.