Tanqueray is considered a premiere brand. The next premium is
Bombay Sapphire.
It is good to Start with Gordon's or Beefeater and work from
there.
I personally prefer Gordon's for the hint of sweetness and
blackthorn fruit.
The reason why you should start with Gordon and Beefeater Gin is
because :
Cheaper
Characteristics and taste is milder and more generally
accepted
Good for cocktail mixes.
Premium Gin are good for :
Premium Martinis/cocktails
Drinking Neat
Drinking On The Rocks
If you like Gin, you may then try to get the premiums. I find
Bombay Sapphire delightful. But Gordon's will have the 'punch or
kick' of Gin.
Cheers