You don't have any criminal convictions so you can tick 'no'.
It might be an idea to disclose your speeding tickets/disqualifications etc. anyway though - perhaps in the Additional Information section or in a cover letter, just to be honest.
We did have one person who disclosed a conviction she thought was spent (because it had been more than 5 years), but it turned out it wouldn't be spent for 10 years and so resulted in a visa refusal.
Now, luckily she disclosed it even though she thought she didn't need to, which was a good thing because if she hadn't, and then they discovered she had the conviction, she could have been accused of using deception in a visa application and banned from entering the UK for 10 years. As it was, the visa was simply refused and she just had to wait until it was spent before she could apply again.
So, that's why I suggest disclosing everything even if you don't think it matters, just in case.