Try to buy cheese that contains as few ingredients as possible. You don't want a lot of starchy fillers and thickeners. Just remember, the fewer ingredients the better -- just milk, salt and enzymes are best -- but if there is a small amount of annatto for color, this is better than a lot of artificial ingredients. You also want to make sure the cheese you choose is made from pasteurized milk products to avoid possibly harmful bacteria that can cause illness (like listeria). Harder cheeses (like Swiss or Parmesan) are also less likely to carry a risk of listeria contamination. In addition, your child needs all the fat dairy can offer right now, so go for full-fat cheeses. Luckily, these aren't too hard to find.
Make sure you grate or crumble the cheese into pieces that will not cause choking rather than cutting it into large square chunks. Melting cheese onto toast or a tortilla and then cutting it up is also a toddler favorite.