When you are a rookie, you need to pay your dues somewhere. Stay at your first company for at least one year. Pick up and deliver on time. DO NOT HIT ANYTHING. Do not get any tickets or violations. That will put you in a much better position to choose the company you would like to work for. Unfortunately, over 90% of new drivers never even last a year. Don't be one of those guys. Good luck!
Nay, don't bother with the paying your dues nonsense. If you work for a crap company you'll likely quit in the first year. Companies are desperate for drivers. Some will take new drivers if you meet the rest of their requirements.
Take advantage of the current job market. Apply to jobs that are beyond your skill level then work hard to learn the skills needed.