Radiant doesn't use radiation...it is just another name for heat. Basically, the glass top is heated and that heat is what is transferred to your cookware. Induction isn't like microwave technology either, but rather uses magnetic energy to heat the cookware directly - the cooktop isn't heated, though it does get hot directly under the pan when the pan transfers its heat to the cooktop. I love my induction cooktop and my convection oven. We are going induction again in our new home. If it is safety that is your concern, I wouldn't worry about induction or radiant. Good luck deciding what to do.

A coil range is also a type of radiant range.

While I totally understand preferring a coil range to a glass-topped radiant range, the sad fact is that nobody makes a good coil range anymore. Any new coil range is going to be pure bottom-of-the-line junk. Unless you want to look around for an old one and restore it, I would cross coils off your list. When you go to look at ranges, just give the side of a new coil range a little push and see what happens.

Induction is a no brainer if price is not a concern.

Better range of heat, much higher high temps, lower consistent lows, and faster too.

You will need induction compliant cookware.

Some young people, particularly teenagers, can be annoyed by a buzzing sound induction can make. Almost no one over 40 can hear this.

IMO, teenager repellent is a plus :)

The radiant smoothtop heats the glass to 800* or so. This bakes anything on like paint. It's hard to keep clean. Induction warms the surface from pan heat. It's no where near as hot and spills can be wiped off.