really you just need to have it setup so that there is airflow doesn't really matter how it happens -- but remember hot air tend to rise so the best airflow would be to pull in fresh air from towards the bottom front of the system and push the hot air out from the top back of the system with it flowing across the parts that are putting out the heat. whether you need fans to assist in the air movement or just openings that let it circulate depends on the setup and hardware used (ie. higher end GPUs will put out much more heat than lower end)
For most bartops there will be a few fans on the hardware already that will move air across the most vulnerable parts (CPU cooler, GPU fan, etc.) so mainly you just need to ensure that there is a means for the hot air to escape (ie. a fan placed toward the top back of the bartop) and a source of fresh cool air to be sucked in from the outside, whether it is just the gaps in the build or actual openings made for that purpose.
So best method is to have any fans located toward the bottom of the system be set to pull air into the system and any located toward the top of the system set to push air out.