What steps should I take to make sure I am not being short changed or
paying for unwanted retirement plans?
Almost certainly, this was simply a case of confusion.
Talk to HR, explain what you wanted to do, and learn what you can do now.
In many of the public employee retirement systems these days, there is a default selection. In your case, enrollment at the standard 10% level was likely the default. If you wanted a different action, there would be forms to fill out indicating your selection. It sounds like this wasn't clear during the onboarding process.
Most systems have a certain period of time to complete this enrollment, such as 120 days from the start of employment. You may still have time to change your selection.
As far as "getting your money back" that may also be a misunderstanding. Once money is put into a retirement system there are ways to get that money out, but most involve a penalty and perhaps a tax hit. Perhaps what they were saying is that when you separate from this company, you can roll over the money in your retirement account to something like an IRA if you don't want to leave it in place. Again, check with HR.
If you are in a public employee's union, your union can also help.
(As an aside, public employee retirement systems are often very generous in their matching amounts - more so than private employers. You might wish to talk with a financial planner to consider if saving for retirement this way is in your best interest.)
Being promised $X virtually always means a gross amount, not a net amount. Out of $X must come taxes, the employee's cost of benefits, etc. In this case, it doesn't sound like the employer was trying to be intentionally misleading, but perhaps didn't convey enough details for you to understand.
If after discussion the entire package is less than you were hoping, you can always find a new job then quit this one.