Usually the parent who has done most of the parenting will get physical custody. There is often little marital property to speak of, and if there is, it is often possible to split it up according to how long the marriage lasted and who contributed what.
If this is the case, the couple should try to set aside their bitterness and take advantage of what is commonly known as a 1A divorce. The parties' attorneys put together relatively simple pleadings that state they have irreconcilable differences, and then submit those to the court along with an agreement outlining child custody, visitation and property settlement. They can get a court date and a divorce within a few months.
It's still a good idea to have attorneys involved in the process, but the legal fees will be far less than if they decide fight over something that is a forgone conclusion to start with.
There are some issues worth fighting over, such as alimony, sorting out particularly complex financial circumstances, or moving the children out-of-state.
By all means, fight if there's a reason too. If not, it might be a good idea for both sides to finally stop the bickering and work together.