Now over my course of study in the Harry Potter Realm of wand making, there are things J.K. Rowling based her ideas of how she could organize who got what type of wand. I have compiled a lot of her thoughts and a bit of my own to create a logical and mathematical way of finding the perfect wand.
First off it the wood type, Rowling has said on many occasions at first it was completely random, and she really only specified Harry and a couple others wands, and later found under the Celtic wand system that was based on birthday, Harry's wand would still be Holly, and so she started incorporating that second book on. So this is the most accurate Celtic chart I can find
Jan 21 - Feb 17 Rowan
Feb 18 - Mar 17 Ash
Mar 18 - Apr 14 Alder
Apr 15 - May 12 Willow
May 13 - Jun 9 Hawthorn
Jun 10 - Jul 7 Oak
Jul 8 - Aug 4 Holly
Aug 5 - Sep 1 Hazel
Sep 2 - Sep 29 Vine
Sep 30 - Oct 27 Ivy
Oct 28 - Nov 24 Reed
Nov 25 - Dec 23 Elder
Dec 24 - Jan 20 Birch
Next would be the core, the most common way I found to tell is by the moon cycles on the day of birth. This is solely fan info I found and no comments from Rowling. Select the one closest to when you were born. Also remember Ollivander does not like using all of these cores, so you might need to go out of your way to get the others.
New Moon - Basilisk Scale
Waxing Crescent - Acromantula web
First Quarter - Unicorn Hair
Waxing Gibbous - Fairy Wing
Full Moon - Phoenix Tail Feather
Waning Gibbous - Veela Hair
Third Quarter - Dragon Heartstring
Waning Crescent - Boggart Essence
For American Wizards (Optional)
Waxing Crescent to First Quarter - Wampus Cat Hair
Waxing Gibbous to Full Moon - Thunderbird Tail Feather
Waning Gibbous to Third Quarter - White River Monster Spine
Waning Crescent to New Moon - Rougarou Hair
Now the sizing chart is a beast of my invention and in no way shape or form is the opinions of J.K. Rowling, it just has the mad genius kooky feel of the wizarding world.
Height (in inches) + thumb size (in inches) + hat size (rounded to nearest half) + pinky size (in inches) + lucky number. Take that number and divide it by 9 and there it is! If it seems abnormally small or big, you may roll a 100 sided dice (or two 10 sided dice, so if you roll a 4 and a 7 it can be 47 or 74, two zeros being 100) and add or subtract that before the division.
I currently have no system on its flexibility but will add one when I find something reliable! However someone wrote up definitions on what they think they may symbolize on the link
I will now provide my wand stats as an example
My birthday is in late July, giving me a Holly wand, born under a third quarter moon so my core is Dragon Heartstring, after my calculations it came to 15 1/2 inches in length.
Now I thought this was an intriguing way of doing your own Ollivander's style business. Then when I went to the Wizarding World of Harry Potter in Orlando, I went to Ollivander's to see what my wand really was. You can guess my surprise when he gave me a wand that was Holly, Dragon Heartstring, slightly springy and measured to exactly 15 1/2 inches!
My thought instantly went to there is no coincidences and led me to euphoria in finding an accurate way of guessing at least my personal wand! So I want to provide this with everyone and cannot wait to see your results! You can also use this for your roleplays to get fun results of wand combinations!