If your kids watch TV a lot, 37 inches will be better. 42 inches TV will get them dizzy easily because it is too big for them. Both LCD and Plasma TVs do not have radiation problem is CRT TV, so they are OK for your kids. LCD TVs consume less electricity. But the picture quality is not that good as Plasma. But if you TV will face to window and even sunlight, it is better to use LCD as Plasma TV will have the problem of light reflection. However, the lifespan of Plasma is shorter.
Depending on your budget, you can try for Teac, Prima, BenQ (LCD TVs) for less budget, Sony, Samsung, Hitachi, Sharp, Fujitsu and LG (LCD or Plasma) for more budget.