I used to have something similar, many years ago but when I was teaching my daughter basic electronics I went for something like this.
Much more flexible as you can choose components not in a kit and get them from stockists like Farnell or Radio Shack, if that is still going. It is also modular.
You need a few basic tools, pliers, cutters, a multi-meter and something to supply power (a small bench power supply or battery will do). If you want to get more advanced it starts to get expensive but is a good start. I am an electronics design consultant so my lab is much more extensive but this is a good way to start small
For software I am a big fan of the Arduino: A small single board computer with a very simple OS and decent libraries available to get you started. You can learn programming from the ground up and get a proper understanding of the hardware without being over burdened by Linux or Windows which while both are powerful neither really suits beginners unless you just want to play with very basic concepts using something like scratch.