In creating a wizard character, it can become important to the design of your character to know what kind of a wand your character carries. There are goo gobs of wand generator sites on the web that you can choose from, but please remember, that none of us here on PA will ever have wands like the Elder wand. None of us will ever have that sort of power here in the world of PA.
So, to give you a bit of a hand, I'm providing here some links to some of the wand generators. These first few are sites that have the HP canon in mind in their design.
http://www.fantasynamegenerators.com/wand-descriptions.php#.WUz7x7pFyM8
http://www.springhole.net/writing_roleplaying_randomators/magicwand.htm
The ever helpful Wiki has a number of helps on designing your own wand. For example, here's a list of wand woods: http://harrypotter.wikia.com/wiki/Wand_wood
and, a list of wand cores:
http://harrypotter.wikia.com/wiki/Wand_core
Or--you could very well try to generate your wand more authentically to how it was done in canon--according to th wood that was associated with the date of birth of your character, as deteremined by the 13 month Celtic tree calendar. Here's the gist of what you need to know about months and woods. Find your wood, then go to the wiki wand wood list if you want to find out what the characteristics are of each wood. NOTE: Yes, you can have an elder wand, but NOOOO you cannot have that elder wand.
Birch Moon: December 24 - January 20
Rowan Moon: January 21 - February 17
Ash Moon: February 18 - March 17
Alder Moon: March 18 - April 14
Willow Moon: April 15 - May 12
Hawthorn Moon: May 13 - June 9
Oak Moon: June 10 - July 7
Holly Moon: July 8 - August 4
Hazel Moon: August 5 - September 1
Vine Moon: September 2 - September 29
Ivy Moon: September 30 - October 27
Reed Moon: October 28 - November 23
Elder Moon: November 24 - December 23
(Thanks to Thought Co.and Patti Wigington for the information on the Celtic Calendar)