Best way to generate order numbers for an online store?

Every order in my online store (lil peep crop-top) has a user-facing order number. I'm wondering the best way to generate them. Criteria include:

• Short
• Easy to say over the phone (e.g., "m" and "n" are ambiguous)
• Unique Checksum (overkill? Useful?)

Doesn't reveal how many total orders there have been (a customer might find it unnerving to make your 3rd order) Right now I'm using the following method (no checksum):

Right now I'm using the following method (no checksum):

def generate_number                
    possible_values = 'abfhijlqrstuxy'.upcase.split('') | '123456789'.split('')

    record = true
    while record
        random = Array.new(5){possible_values[rand(possible_values.size)]}.join
        record = Order.find(:first, :conditions => ["number = ?", random])
    end          
    self.number = random
end