If you have the money, it might be worth getting a full psycho-Ed assessment done, so that you have an accurate picture of what his strengths and weaknesses are, and what supports would be a good idea. Then you can use that info to search for settings that can provide what he needs.
For mild ADHD, you are unlikely to get a lot of support in state, tbh.
Usually for kids with mild difficulties, it is yr 3 ish that the differences with their peers start to become unavoidable, and the school starts to wonder and put them on waiting lists for assessment (can be a year or so on the list). So if you have definite concerns and suspect that a diagnosis is likely, I would take the bull by the horns and get onto it.
Discuss with your go or pediatrician (in the next year or so if he is carrying an ADHD diagnosis and needs support in some areas, it may be worth discussing medication, but whether this is something you would consider or not, if you believe your son may end up with a dx, it's worth getting your gp/ paed to start the ball rolling.
Sometimes private settings are better as they have more sporting facilities etc (and usually daily pe), but you need to look at the academic requirements and decide whether each setting matches your son's needs. As others have said, discussion with the senco can be helpful, but without a dx, it is unlikely you will get far.