Here's a little something from another Harry Potter board. It lists different wood types and cores. Feel free to consult when creating a wand for your character. Please be aware that wand lengths are proportional to height with short wands being 7.75 to 8.75 inches (people under 5'2) and long wands being 11.5 to 14 inches (people over 5'10/11). (Info on lengths found by Carrie)

December 24-January 20 = Birch
January 21-February 17=Rowan
February 18-March 17=Ash
March 18-April 14=Alder
April 15-May 12=Willow
May 13-June 9=Hawthorn
June 10-July 7=Oak
July 8-August 4=Holly
August 5-September 1=Hazel
September 2-September 29=Vine
September 30-October 27=Ivy
October 28-November 24=Reed
November 25-December 23=Elder

Other wood types include yew, blackthorn, rosewood, ebony or ivory.

Other than the standard Unicorn tail hair, Dragon heartstring or phoenix feather cores can also include;
Feather of an Abraxan – these are winged horses that are bred by Madame Maxine of Beauxbatons. Best used for charm spells.
Feather of an Augury (Irish Phoenix) – The Irish Phoenix’s call predicts heavy rain – best used for Divination spells
Scale of a Beetle – standard scarab beetles can be found across the world – best used for potions
Fur from a Sphinx – best for defensive spells

*If your wand contains a phoenix feather, it may not be from Fawkes. Veela hair cores may only be used by those playing Victorie, Jacqueline and Alina Weasley as they have a veela ancestress.*

Credit for this information goes to Chris from The Sweetest Nightmare.