Setting up and Cold Calling Leads with more than 2 phone numbers?

Setting up and Cold Calling Leads with more than 2 phone numbers?

We are cold calling people. When a lead comes in it has a list of 1-12 possible phone numbers that might work for that lead.  Our leads utilize the built-in "Mobile" and "Phone" fields along with 10 custom phone number fields. We have to manually dial each number and use our cell phone to call.

Each lead will use 1-12 of these fields:
  1. Phone
  2. Mobile
  3. Phone #3
  4. Phone #4
  5. Phone #5
  6. Phone #6
  7. Phone #7
  8. Phone #8
  9. Phone #9
  10. Phone #10
  11. Phone #11
  12. Phone #12
There has to be a better way than this because I'm sure we're not the only company calling more than 2 numbers per lead, right?

My questions are:
  1. What would be the wisest way to store 12 numbers attached to a lead that we can cold call? 
  2. What telephony plugin would be best (and inexpensive) to use for this setup? (eg. something that lets us click to call and tracks each outgoing call and the result). It could use a Voip number or our cell, doesn't matter.
Can anyone recommend something they use and like?