I think Java is a good election. But, please, buy a book. There are very good manual's online, but I can tell you it's easier to force yourself to learn if you buy a book, and it will force you to code more (no copy&paste). If it's a good book, it would explain you the basic algorithms. There's no need of learning complex or optimized algorithms at the start. You would be surprised of all the things can be done with the basics learnt in a few days... Hell, I coded a bmp image editor (rotate and scalate imagens, basic drawing, image filters and so on) with basic knowledge of C and without copy paste! (It took me 50-60 hours though)
It's true that C/C++ are THE programing codes, but I think you should learn them only if you are going to use them proffesionally. Sure, in C programs work faster and have less errors than others (as C doesn't tolerate errors like other languajes), but I don't think you should start the hard way.
If you want to see results, Java is the way to go. It's relatively easy to learn (not for me, I found C easier xD, but it is because I am accostumed to work at a very low level) and you will see relatively complex programs soon.
What's more, altough many will jump at me, the fact that Java uses more resources than C it's not an actual defect... Come on, we have 4 Core processors for 100$/€... there's plenty of potential to waste! 
. In terms of learning a language this has no importance at all... only if you program professionally this will start to matter more. And, if you do this (to program professionally), you won't use the languaje you want, but the languaje the work imposes you.
For example, I code in C and Assembler, but that is because I program microcontrollers, from 8 to 32 bits, and there, size an resources matter a lot (speciallly in 8bit microcontrollers, Assembler it's nearly compulsory). But if I worked with online apps, Java, php, asp, xhtml or Javascript would be my languajes.
Good luck!
PS: You can ask me if you have troubles.... with C or Assembler. I can't help you with Java, as I almost never used it.
