One thing to keep in mind is that accidents occurring more than 5 years in the past should have no impact
on your current insurance rates, so you are definitely outside of that window. Concerning your speeding ticket, if you have not yet been to court then it most likely has not been added to your driving record, meaning you shouldn't be penalized for the violation if you purchase insurance coverage before your court date. You should also qualify for a prior insurance discount when you look for a new policy since you are listed as a driver on your dad's insurance, assuming it has been at least six months
. You potentially have a clean driving record, as far as an insurance company is concerned, and you're currently insured, so finding affordable coverage should not be a difficult task. Rates vary by company and are based on many different variables, so your best bet to find the lowest rate is to get quotes
with as many companies as possible. The same advice about shopping around goes for your dad as well.
P.S. make sure your dad does not remove you from his policy until you get your own coverage because you will lose the prior insurance discount.