As you probably know, induction burners produce an alternating magnetic field that induces a current in the cookware. This process can produce attractive and repulsive forces as well that cause vibrations.
The problem can be caused not only by poor sandwiched construction but by an uneven bottom surface, or loose parts or lids.
I have read that some people have successfully used silicon baking pads to dampen the sound.
This page has some useful information on the subject:
http://theinductionsite.com/proandcon.shtml
Toaster ovens are awesome. For a toaster oven, there are three key features:
- Big enough to fit the largest item you'll cook.
- Convection, so food cooks quickly and evenly.
- Enameled or stainless/aluminum interior. This lets you use harsh abrasives to keep it clean.
It's a given that your oven should have bake, broil, and roast modes.
For size, you'll probably want it big enough to comfortable fit a 1/4 sheet pan, or a 9" x 12" brownie pan. That will allow you to bake. Much bigger and it will take up a huge amount of counter space and realistically you should use a full oven for the big stuff. Too small and you'll have to fire up the full oven for everything, which defeats the purpose.
Convection makes a huge difference in toaster ovens; because they're so small, they are more prone to uneven heating than normal ovens, and leak heat out the front. If you open them to move food, they'll lose most of the heat, and take a while to get back up to temperature without convection. Convection lets you cook faster and more evenly.
For cleaning and long-term use, you need to be able to scour off the burned-on crap with steel wool or other harsh abrasive. Otherwise the oven will quickly become so unsanitary that it must be replaced, and nonstick finishes never last. The bottom will, of course, be lined with aluminum foil for easy cleanup of drips.
Oh, and rotisserie is a useless gimmick. I've had it on ovens, and never used it yet. Other people may have different experiences with it, of course, but that's my $0.10.
Best Answer
The Great British Baking Show is actually the Great British Bake-Off, they seem to change the name when it goes onto PBS for some reason. The ovens they use are Neff "slide and hide" models with multiple settings. The fan mode is convection mode. If you don't have a convection mode the recommendation is to increase your temperature by 15 degrees C, or about 30 degrees F. Conversely if you have a convection oven and you want to use a non-convection recipe you'd drop the temperature by the same amount.