Herb Garden Must Haves!

Z and I used to have a beautiful mint plant. It was hearty and lush and provided the perfect leaf for hubby's mint juleps. Then we were hit HARD with a slue of storms and destructive puppies and the mint is no more. The same thing happened with my first basil sprout. He blessed us with quite a few pesto nights but once I plucked him clean it took forever to get enough new leaves for another batch. He was also destroyed by raging rainfall and psychotic Boston Terriers.
I'm currently planning a bigger and better herb garden {something like the photo below}and would love some tips from those of you that have your own.

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~What are your fail-safe tips for keeping herbs alive and vibrant?
~What are some MUST have herbs that your kitchen couldn't live without?
~Where do you keep your herb garden?
~Which herbs are the heartiest and which need a more gentle looking after?
PLEASE HELP!
I'm really eager to get this started and while I could research until I turn blue, I wanted to come to you, my blogger friends, for some first hand advice!
Until next time...
Thanks in advance for all your tips, tricks and thoughts!!