You need the usb cable to program the board, the sd card is optional to store data.
But before you can upload your sketch to the board you need to install the autonomo in the arduino ide.
Can you follow the instructions on autonomo.sodaq.net
The LiPo and solar panel can be connected inthe order you want.
The Lipo is charging from both Solar panel and usb, you can connect them at the same time!
When the lipo is fully charged the charge led will turn off.
Let me know if the installation works, and that basic sketched like the blink sketch are working. Then I will help you to connect the sensors / leds
For you to start with don't use the switches row yet.
Change A0 in the code to A2, A6 or A10.
Change this in the code, in most of the tutorials you find online they use Serial as the debugline, this is for all "old" arduino boards, you need to change Serial into SerialUSB to get feedback in the Serial Monitor.
The Autonomo has 3 types of connection: Analog ports, for every analog sensor. defined as A0, A1 etc
Digital ports, D1, D2.. etc
And one I2C bus. On the shield you see SCL SDA.
I hope this helps you, let me know if you get everything working