Probation is common in first-time domestic assault cases. With probation, the judge sentences you to a jail term and/or fine and suspends part or all of the sentence. So you may have to pay the portion of the fine that is not suspended. A big concern with domestic violence cases is the possibility of a protective order. If a protective order is issued against you, you may have to relocate. Penalties for violating these orders can be severe. In many jurisdiction, the court will also require you to go through a treatment program or attend classes on domestic violence as part of your sentence or conditions of probation.
With regard to your question regarding sufficient proof, the prosecution does have evidence- they have your boyfriend's statements to the police. He may recant what he originally told the police, but the prosecutor still has the original statement and could allege that a recantation is fabricated. People get charged and convicted of crimes all the time based on nothing more than the alleged victim's testimony or statements to the police. Granted the prosecution's case would be much stronger if their were additional witnesses and photos of injuries, the alleged victim's statements are all that is necessary to convict someone of a crime.
It is possible that the prosecutor will dismiss the case if your boyfriend recants, but do not count on that. You should contact a criminal defense lawyer in your state before your first court date.