Tack cloths are ok, I have used them, but to me, nothing picks up dust better than a damp cloth. And absolutely do it after each light sanding, this is when its the most important. Just because there is water involved doesn't mean its going to destroy the surface or cause issues with paint adhering. You can light sand, use a damp cloth to wipe it down, and paint in 5 minutes. Were not talking a soaking rag here, just take a cotton cloth and get it damp, then just wring its neck until all the water is squeezed out. You can then use that to wipe down your lightly sanded surface and it will pick up any traces of dust.
I have used this for years on wood finishes, from floors to desks, to my cabinet (which is MDF) and it works great.