You might want to get what's called a practice shoe. They are the most comfortable and supportive, especially if you have foot problems. Unless you are planning to compete, you can really wear any shoe that's comfortable for you.
My favorite is the Elegance Godiva practice shoe. It's a mostly closed shoe with a small open toe and is a lot prettier than most practice shoes. You can find it at dancehappy.com.
If you want to get a closed shoe, you can get a shoe designed for Standard or Smooth style dancing. Standard shoes are closed pumps and Smooth shoes have closed toes and heels with open sides. What are strictly called "character" shoes are not ballroom shoes and I've heard they are not balanced in the best way for ballroom dancing.
If you do want to get a sandal-style Latin shoe, Celebrity shoes allows you to order shoes with a choice of heels, some of which are lower and wider than the typical Latin shoe. As a beginner, I used the "Monet" heel which was very stable.
Just make sure that your shoes are comfortable and you feel stable on them. You need to take good care of your feet!