I filed for an uncontested divorce also!! It's the cheapest way to go when you have nothing to split up or there's no finger pointing!!! And yes, you pay as you go! The attorney will send you paper work one step at a time you pay and send it back and he files it and sends you the next step and so on!! Some steps have time limits that you must wait before the next step can be taken!!! It's def the way to go, but your ex needs to be on board with it also or it will not work out!!
I paid a place that files all the paperwork for you and I had to pay up front for it. It saved me a lot of money because I didn't have any issues or someone who would contest it so i didnt need to hire a lawyer. If your using a lawyer then it becomes part of his fees and if your judgement against your ex is for paying court costs then this would be part of it. You still have some up front costs either way.
Each county sets its own fees depending on their legal provision. There are several types of costs involved in filing a divorce such as service of process fee. I would suggest that you consult your lawyer for more professional help.