By the way , i came from Germany and sr about my bad school english. :)
If that is bad then you should have no trouble at all.
The Arduino site has many pages worth bookmarking. Here is the official libraries and software serial page:
What Arduino to get? One that you can use to program stand-alone AVR chips for projects and test code with!
Arduino is a development board. You will also want a breadboard, jumpers and other bits.
One Arduino can let you build many projects while keeping the Arduino itself.
The UNO is one good choice because it has a low-cost medium ability chip in socket, you can change the chip on the board for another with bootloader burned in (can buy pre-loaded, maybe 2 or 3 Eu) and program that right on the board then take it off and plug it in elsewhere.
But buy at least ONE genuine (not super-cheap clone) Arduino please, just to support the support you get!
This page shows how to build and program both 328P and 1284P (16K RAM, 2 hardware serial) 'duino's.
How to make an Arduino-compatible minimal board
If you don't much at all there are smaller AVR's that IDE files are available for, down to 8-pin ATtiny chips.