I was interviewed during the investigation and I told them the truth - I didn't hide anything.
Especially as an unskilled worker, many companies would rather terminate an employee in a misconduct HR case than look for other solutions. Generally they cite liability.
It's the impact on my resume that I am most worried about - whether it's better to be the one who quit vs. being terminated.
Your next job will ask you why you quit or were let go. They will also call the previous company and verify employment dates and termination. You need to be ready to answer this question honestly, and in such a way that implies you won't do it again.
If the "misconduct" was something specific to the job, such as "Operated heavy machinery without a permit," then the answers is easy. Simply find a job in an industry with fewer regulations where the "misconduct" wouldn't have been an issue. For example, "I was let go for failing to follow regulation XYZ, which is why I've decided to pursue jobs in retail"
If the misconduct was something such as sexual harassment, drug or alcohol abuse, or stealing, the answer becomes more difficult. You'll still need to be prepared for future hiring managers to know about the misconduct, and have an answer ready. Here are some ideas that may help.
1) Consider leaving this position off your resume and find a job in a different industry. Be ready to be let go if this comes to light during your employment.
2) Quit now and when asked say the position wasn't a good fit. I'd also look for jobs outside of that industry as if the new job finds out you were about to be fired for incompetence, you'll be let go.
3) If the issue was drug- or alcohol-related, and this has been a wake-up call, then consider joining a support group. Although it will not help immediately, in the future, you can show that you have changed. Not everyone will be willing to give you a second chance.