When I started programming, I loved computer games. So I started writing my own games, as soon as I had any tools at hand to do so.
Quite naturally, my very first game was a text adventure. Similarly, you could start with a quiz or something, or some sort of guessing games.
Also, you could start with something, like a slot machine (you don't really need the animations, or even pictures. Just use A = apple, L = lemon, S = start, P = Plum etc.).
This will teach you the basics of handling some user input, maintaining game state and generating output accordingly.
I headed down this road quite far. I progressively learned, how to read out the keyboard state, or the mouse, how to use graphics code. I learned more about the language itself (I started with PASCAL) and used this to enhance my existing games or just started something new.
I think games are really great to learn programming. Even with little experience, you can create small things, that give you small moments of pride. Because you create something, that's fun. Building actual applications is quite pointless, because it takes a lot of work to create something, that is actually useful, whereas it is surprisingly simple, to create a small game, that turns out addictive.
You may want to actually use an educational language (in my case, this was PASCAL and in retrospective, I think it proved to be quite a good choice). A lot of them are specifically aimed at creating games and such.
Creating applications is more than just creating algorithms. You have to design features, you need to organize and structure your code in different layers and modules. Unlike the rather "atomic" problems you're given at university, applications are sometimes best developed in an incremental way. You start with something and you add things on top of it. Thus already having something to start with (as you would in some of the languages listed in the wikipedia article), you save yourself a lot of frustration and start creating something right away. (A colleague of mine started programming by writing quake 2 mods). At some point, you will come to find the limitations of these easy-to-use tools, but until then, you will have a lot more insight and understanding. Probably enough, to reimplement the functionality they gave you to start with yourself.