Photography sessions of young children can be done in a studio set up or on a location. Younger children, especially if they are the only subjects, usually photograph well with a non descript background. But as they get older or if you want a more "active" life style kind of image then working on location will yield better results.
The standard has always been to have neutral colors with regards to clothing but many parents now are more interested in "real life" clothes. What you want to consider is will the clothing be a distraction? Years from now will the image still look current? I have a 20x24 of my oldest son hanging above our fireplace that was shot when he was 9 years old. He's walking along a creek wearing white shorts and a white shirt. He's now 27 and you'd think it was taken last week.