I'm only going to talk about this generically. There are many makers out there and we all have our likes and dislikes. I'm sure you'll get lots of thoughts.
There are a number of issues to consider.
Gas or electric:
Most people prefer gas for its responsiveness. Electric devotees like the preciseness. In a cooktop, gas wins pretty much hands down. Electric is great for melting and other low temperature works because it is so precise. Only ranges with gas simmer burners come close, and even these are not as good at the low temp work as are electric ranges.
In ovens, however, it is a whole different story. Electric ovens are generally preferred for their even heating and the precision of the temperature.
Electric has many flavors. Gas ... not so much:
Electric coils, well, everyone is familiar with these. They're not terribly responsive and they tend to stay hot, even after they lose the red glow. With little kids, this could be an issue. If something boils over or simply gets too hot, you have to move the pan; lowering the setting has no immediate effect. You also need to have pans with smooth, flat bottoms for them to work well (they work mostly by direct contact). Warped pans won't work as well. Forget woks.
Ceramic tops work by several methods. Some are infrared. Some use halogen bulbs. Some use plain old metal coils located below the glass/ceramic top. Generally they function much like metal coil ranges, but do so based on several different principles of physics. As a practical matter, however, they're all pretty much the same.
Induction Cooking:
This is a whole new cooking method. It works on magnetic principles. The 'burner' is really a special kind of magnet that excites electrons in the cookware itself, causing the pan to heat, not the 'burner'. I put 'buner' in quotes, because it is not at all a burner in the conventional sense. In fact, the 'burner' never even gets hot. Only the pan gets hot. It is as responsive and precise as gas, as efficient as electric, and as capable of low temp work as anything out there. The ranges have no open burners, so they're nearly as easy to clean as a ceramic top.
The downside? Cost. They're very pricey. They also require special cookware. That said, it is a safe bet that a fair amount of anyone's existing cookware will work with it. But not all of it. Glass cookware (Corningware, Visions, Chantal, etc.) won't work. Some stainless will work, some won't (depends on the core's or encapsulated disk's material). Woks won't work unless you have (literally) a wok-shaped 'burner'.
In my estimation, induction cooking is the very best of all worlds ..... if you can afford it. I suspect it will get cheaper and cheaper and will replace gas ranges as the price points get in line and fuel costs go up. It has made great inroads in commercial cooking.
Ovens - to convect or not to convect:
Convection ovens are generally better than thermal (conventional) ovens because they have a fan that circulates the air in the oven. This has the effect of eliminating hot spots and allowing the same input of heat to do more work. You can generally cook faster, and at a lower temperature, with convection. However, all is not peaches and cream. Convection ovens play hell with some baking. They also tend to dry out some items you'd rather stayed moist. The response from the industry has been combination convection/thermal ovens. You use the fan ... or not ..... depending on what's cooking. That's my choice. And it is what I have in my house.
As to gas or electric, I'd give a slight edge to electric, for reasons cited above. Also, if you want convection, the choices are far wider in electric than in gas. Notice the rise in the availability of so called 'dual fuel' appliances. In general, this means they have gas cooktops and electric ovens. I also dare say that any dual fuel appliance has a combination (convection/thermal) oven.
So there you have it, Stinky the Clown's Short Course in Arcane and Uneeded Cooking Appliance Knowledge.
And worth exactly what you paid for it .... which is nothing! :)
Anyway, have fun shopping and researching. Lemme know if you have any other questions. I really am happy to answer as I am able.