Gardens of the moon is sort of required for Memories of Ice. A lot of the characters pivotal in Memories of Ice are introduced in the Gardens of the Moon.
If Malazan book of the fallen is for you, you'll know after reading book 2.
Although, in all honesty: I wouldn't start with Deadhouse Gates. Although it contains one of the best plotlines in the series, it also contains the worst character, and she drags stuff down a lot. Were it not for having read through the first book, I would've probably stopped because of her.
The first book has context that I'd say is required to fully enjoy the third book. So, second->first->third->...
Most the downside of the first book is the quality of the writing; it was written before author really nailed the formula. If you like the second book, the first book will be fine because you get fed more nuggets of information about the broader setting.
If Malazan book of the fallen is for you, you'll know after reading book 2.
Although, in all honesty: I wouldn't start with Deadhouse Gates. Although it contains one of the best plotlines in the series, it also contains the worst character, and she drags stuff down a lot. Were it not for having read through the first book, I would've probably stopped because of her.