The Fenix Shillboy
Join Date: Aug 2007
Location: League City, Texas
Bikes: Raleigh F500 mountain bike and an exceptionally old (mid-60's) Schwinn Collegiate 5-speed.
I'll take it from reverse and advise you to start off with Planet Bike Super Flash tail lights. They're just under $18 each via Amazon.com right now and I THINK with free shipping if you spend more than $25 (although the shipping deal changes on a daily basis, it seems, unless you are an Amazon Prime member). You won't get more bang for your buck than with the Super Flash, and the tail light junk that can be had for less than those is usually just that (junk)...don't trust your kids lives to the poor stuff. These things really work and are some of the most highly though of tail lights among forum members here (especially for the price).
Planet Bike Super Flash at Amazon.com
Me, I use flashlights as headlights which enables me to use my headlights as flashlights.
I'm sure there will be lots of dedicated bike headlight suggestions for you, but I personally don't know a whole lot about dedicated headlights so I don't consider myself very well qualified to make a reasonable suggestion for one.
As 10 Wheels
suggested, if you had a rough budget in mind, people could give you "best buy" ideas in whatever your budget category is. $30 for the combo? $75? $100? Everybody seems to have a different idea of what constitutes "reasonably cheap and durable," I think.