In my experience, the best approach to a Mandarin start is to immediately consider how many terminal actions you want and then see if Mandarin fits into that. Because of Mandarin's top-decking ability, if you want Mandarin, you can then probably add one more Terminal to your count. The other useful thing about a Mandarin opening is getting the Mandarin and another card that you want (see Hunting Party/Mandarin
http://dominionstrategy.com/2012/01/09/combo-of-the-day-27-hunting-partyx/). In your game, the other useful card would have to be a $3 because of the lack of non-Mandarin $5 and any $4s. But even getting a $3 can be useful depending on the $3.
However, it's not really a good idea to buy many Mandarins. Even though they allow you to top-deck cards, they are terminals so you probably don't want many. Even 3 in what would then be a deck of 14 cards is probably on the heavy side. The other thing to remember is that Dominion is a fast game and while you're buying Mandarins your opponent is actually using his purchased cards and getting his plan going into a mid-game stage. So, taking even 3 turns on an opening can be dangerous; especially in a game with attacks (which your game didn't have).
So, to summarize, you probably only want one Mandarin during your opening. Getting more than 1 slows you down while your opponent cruises ahead. Also, attacks played on turn 3 could mess up your extended opening. However, Mandarin can help you get some key components early on. Don't go out of your way to buy a lot of them, but keep them in mind when planning your strategy.
