I usually pay three figures for my cars, but I'm crazy. There are plenty of acceptable used cars available in all parts of the U.S. for less than $5,000. Look on Craigslist and Autotrader and try to find private party sales -- used car dealers trading in sub-$5,000 cars in your part of the world are far more prone to ripping people off. Plenty of people here have spoken about makes and models that are particularly good candidates in that price range. Given that your yearly cashflow is around $25,000, my personal recommendation is to shoot for a $2,500 car (more than twice what I pay for my cars), given my hard-core personal rule of thumb that nobody should drive a car worth more than 10% of his or her yearly earnings. At that price point you can still find something adequate, but it is a bit harder than at $5,000.
But more fundamentally, a suspended license due to a long list of traffic infractions (topped off by running a red light due to sheer inattention) is probably the Traffic Gods' way of telling you that you should probably not be driving. Suppose you had your kid in the car when you pulled that stunt and got T-boned by crossing traffic? Also, with that kind of record, your car insurance rates be astronomical. Any kind of driving is a luxury you can barely afford on your yearly income.
So I really think you should try very hard to think outside the box here: pricing out Uber rides, getting very familiar with the bus schedule, figuring out if a bike (even an electric bike) with kid-trailer gets you places fast enough, looking into breaking your lease early to find a place with a better location, even looking for a new job -- it sounds like you are at a server at a higher-class restaurant ($1,800 / month on a part time schedule sounds like you're clearing in the $20+ / hour range, which is far better than fast food), but there are plenty of different neighborhoods in Denver with nicer restaurants that could provide equal wages and a better commute setup.
If you are going to stick with the used-car + restricted license plan, find a used Corolla or Civic or Prius or granny's used Buick from a private seller for well under $5,000. But before jumping into that, spend the rest of the week also figuring out if you can avoid driving for the next few months. And you should probably take some serious driving lessons once you re-qualify for an unrestricted license before getting back on the road.
