Birch has a scooped sound and thats why they say its naturally eq'd. Maple will have the low end and nice highs but will also have more body in the mids. You could go with either because both woods produce a great sound. With all the technolgy in heads you should be able to achieve the sound you're looking for with either wood. As far as kits go I've been fortunate in getting to play on alot of kits both Intermediate and high end and have owned both birch and maple kits so hit me up with any questions you might have. If your looking for a great kit check out
Sonor Force kits. I own one currently and have bought and sold and
Tama Superstar and
a Pearl Session kit while owning the Sonor and its safe to say its my favorite intermediate kit. Other people will have different preferences as well as different experiences with every brand under the sun and there is no right or wrong answer. Out of the two you mentioned I would go with the Gretsch. Be sure to check out Sonor Force though cause if you look around long enough you could probably find a new Force 2007 on the internet for around $600 w hardware. For snares at a reasonable price point (Under $300) I would say:
Black Panther (they come in all different varieties ranging from 150 to 500 bucks new), PDP Ace (around 100-125 bucks used), Sonor Ascent (all Beech and great color options/diecast hoops and comes with Ambassador Top and Bottom which will save you 25 bucks on heads) Theres to many good options to list and with all the equipment it depends on what sound and style you are going for. As far as heads my fav combos are:
Toms - Coated Emps/Clear Ambassadors (Great all around sound for anything other than Jazz)
Coated or Clear Emps/Clear Emps (Sounds Great Mic'd on Birch)
Clear Ec2/G1 (Great for Metal or Punk/Lot of attack but short sustain when you need to hear every note during fast playing)
Snare - Cant go wrong with either Ambassador or Evan Power
Center on any wood snare/Ambassador of Evans Genera Dry on Deep Metal snares
Kick - Remo Powersonic/Aquarian Superkick 2
Let me know if you have any other questions about any potential drum gear! Good Luck!