My compliments to SparkChaser, that is a man that know his gins...
Any of the gins that he suggested are excellent choices. For my tastes, I prefer Bombay Saphire, I think it makes solid martini. Hold off on the small batch gins until you have your mix down. Wasting them is a sin of the first degree.
I have found that the secret to a perfect martini is cracked ice. Use an ice bag or a (clean) dish towel and smack the crap out of it with a BFH or a more kitchen-appropriate tool (big frying pan works well). Open the towel and scoop up all the small shards with your shaker. You should nearly fill it.
Then top off with you gin of chioce. I skip the vermouth in the shaker. Shake well, let sit for a minute or so and pour into a pre-chilled glass.
I keep my vermouth in a little spritzer bottle, one shot into the glass before I pour. Purists (including my parents) think I am overdoing it with the vermouth. They prefer to glance (just a glance) at the vermouth bottle from accross the room and then pour their martini into their glass. If you stare too long you have to start over. Some suggest that you just whisper the word "vermouth" (not too loud now) over top of the glass before you pour and that is sufficient.
Regardless, the real secret to a good ****tail is actually water. The cracked ice melts faster and provides it. If don't have the patience for cracking the ice and you find that your martini is too strong, don't dump it... Add a little splash of spring water, reshake, and try again. You are not watering down your drink, you are making it the traditional way.
BTW, if you making batch martinis for a party, add 1/4 water to your martini mix and put in the freezer before serving, you will get the same effect.
Everyone's tastes are different and no one is right for you except your own.
Good luck on finding your perfect drink.