Personally I'd NEVER, EVER have storage heaters again.
I used to live in a house that had them and boy, what a stupid idea they are!
Basically they consume their energy overnight (on an economy 7 setup) and release their heat throughout the day. They heat up bricks inside and you control the output by way of flappy things that either lets warm air rise out of vents or doesn't let warm air rise out.
They problem with them is that the heat isn't instant, or even quick so if you get caught out by a cold snap you can't just switch them on and feel the benefit within a small space of time. Also, once heated up, you can't switch them off so again, if you get caught out by a warm spell you'll roast in your own home. OK, so you can control the heat output slightly but even if you prevent the warm air rising out of the vents, the heater is still hot and still gives off heat. This also means that you're wasting vast amounts of energy in unwanted heat.
Oh, they're also really bulky.
Convector will give a reasonably quick heat output but may not be beneficial for an Economy 7 setup so you'll be drawing more of your electricity during peak hours.
Depending on the type of convector it is likely to be less bulky than storage.
Can you not opt for slim panel electric radiators on individual timers? Might be a bit better.
Fred