The police never read me my Miranda rights so they don't have a case against me, right?
This is a huge misconception created by TV. Reading someone their Miranda rights, more often than not, has little to no impact on the outcome of a person's criminal case. Generally speaking, the only time police are required to read you your Miranda rights is after they've arrested you AND they intend to ask you questions. The police DO NOT have to "mirandize" you simply because they placed you under arrest.
Apart from this you are better off telling the police you want to speak with a lawyer regardless of whether you've been arrested or not.
I didn't do anything wrong. Can you get my charges dismissed?
There is no good answer for this question. Whether you did something wrong or not may not have any bearing on whether the case will be dismissed. No attorney can promise you the outcome of your case. Sometimes a case may be dismissed but most aren't dismissed once their filed. Even the cases that do get dismissed it is often because you, the defendant, have enlisted the services of an effective defense attorney to help build a solid defense for your case.
Your best course of action is to find an attorney who you can trust as soon as possible and begin working to build a defense.
The alleged victim isn't pressing charges against me so why was I arrested?
Another falsehood perpetuated by TV. Alleged victims don't have the authority to "press charges" or not. Only a prosecutor's office has the authority to make that decision. Sometimes the prosecutor may consider the alleged victim's opinion before they make a decision. However, many people find themselves being prosecuted and convicted by alleged victim's who didn't want to cooperate. If the alleged victim didn't want a prosecution to happen they should have avoided getting the police involved in the first place.
I need a good lawyer. Should I hire my own attorney or use a public defender?
"Good lawyer" is a tough term to define. I would define it as someone who is competent in their profession and cares for their clients. I've met a lot of lawyers - both public defenders and private lawyers. I believe there are both good and bad lawyers and it often has nothing to do with whether the lawyer is a public defender or private attorney. If you qualify for a public defender you do not get to choose who your lawyer is. If you hire your own lawyer you DO get to choose who that person is. So the important thing to consider for this question is whether you want to choose your lawyer or are you agreeable to having one be given to you.
Should I fight this case or just accept a plea bargain?
This is an impossible question to answer at the beginning of ANY case. There are so many variables in play in criminal cases. A lawyer who tells you what you should do before they've had a chance to gather and review the evidence should be treated with skepticism. This is why it is important to find a lawyer who you can be comfortable with and build some trust. Have consultations with a couple of lawyers and ask your questions. Look around online and read reviews and then go with your gut. Defending a criminal case is an important thing in your life - your lawyer should think so too.