Insurance companies could care less if those tickets were on a skateboard. They were moving violations that you were convicted of, end of story.
On top of that if you do not have any driving experience in a Class A vehicle you are going to find it hard enough to get insurance with a clean driving record but with 4 tickets in 3 years you will probably find it impossible. Even if you did find an insurance carrier you probably could not make enough to pay for th truck, fuel, insurance and other operating expenses and still have any money left to pay yourself.
Your best bet is to let 3 of those tickets drop off, go get your Class A liscense through a CDL school, then hire on as a company driver for 2 or 3 years to learn the ins and outs of this biz before jumping into the deep end of the pool as an O/O or Indy.
And just so you can not say no one tried to answer your question you will find 99% of what you want to know about liscencing and such
HERE and the other 1% you can learn by contacting your state department of motor vehicles and the commercial vehicle enforcement office of your state police.