MVR/School

The accident is the biggie; the tickets aren't too much to worry about because they're over 4 yrs. old. Was the accident listed as reckless driving or what and any tickets connected to the wreck?
Where is your location so we know the hiring area you live in.

 

How old are you

 

Probably a dozen or so companies will hire you. Sometimes when you fill out an application online, it will show "Intelliapp" which means you might just fill out one application, then every time you start to fill out one for another company, your intelliapp will pop up already filled out and you just submit it again and it will go to the company whose website you're looking at.
Since your school starts soon, you can begin applying and check "student" on the applications.
Try these for starters and there's plenty more if you want:
Calex Logistics
Freymiller
Nick Strimbu Inc. - Teamsters
PI&I Motor Express - Teamsters
Magnum Ltd.
Tyson Foods
Don Hummer Trucking
Veriha Trucking
Navajo Express
USA Truck
Let us know if you want more names.

 

UPS Freight might hire you; they're OTR and usually gone 2 or 3 days.
Walmart won't hire new grads. Schneider and Swift probably would hire you, but you don't need a company that large, but that's personal choice.
Probably no FedEx either; usually contractors hire the road drivers. They own trucks that are leased to FedEx, but still any drivers they hire must meet FedEx hiring criteria.
Every company I listed hires new grads. If any website has "experience requried", ignore it because the website isn't up to date. Submit as many applications as you want; the more the better.

 

Why are you determined to work for "big name companies"? It's not like getting hired at Google, it's more like getting hired at McDonald's. The pay & working conditions are usually better away from "big name companies."

 

The terminal amenities are a good recruiting tool, but you'll rarely be at a terminal. The mechanics and office people probably really enjoy it though. You can excercise with any company; many drivers do this. Carry a set of 20 lb dumbells and a folding bicycle and will stay in great shape. Showers are free when you buy fuel at a truckstop.