Martinis can be made with vodka, especially in this day and age where they are the norm in many places there's no need to be puritanical.

I had a great Vodka martini made with Russian Imperia in Paris which was the equal of the very best Gin Martinis I've ever had.

That said, in general I prefer to drink vodka on the rocks, maybe with a twist of lemon and use Gin in my martinis. My preferred style is an in-and-out Martini - wash the glass with vermouth and tip it out. Then fill with cold gin (Tanqueray 10, usually about 75mL), and use a couple of olives on a cocktail skewer as a swizzlestick to keep gently stirring.

Usually I drink these like water and can down 5 in my first hour, but if the occasion calls for savouring it, get yourself one of these:

http://awesomedrinks.com/collections...rtini-set-of-2

Fill the bowl with ice water and you can keep your martini chilled for ages.