I will try to collect here information, ideas and my experiences about how to use these "non-arduino-standard" uC as a Standalone and how to be able to programm it with the Arduino IDE and an ISP Programmer / Arduino as ISP for ATtiny.
Why these ATtinys? Because they cost me only around 1-2Euros, have 8, 14 or 20 pins, are low in power consumption and have also ADC and PWM. So they are small and cheap for standalone projects :)
Comparison table of ATtinys, ATmegas... https://www.mikrocontroller.net/articles/AVR_Typen#Weitere_Vergleichstabellen
Very nice example what "standalone" can mean with an Arduino ATmega168. Letting it sleep inbetween working. Called nightingale. With the ATtinys you would not need the external crystal oscillator, they are set to the internal. http://interface.khm.de/index.php/lab/experiments/sleep_watchdog_battery/
First for the ATtiny 13a:
Preparing the IDE: http://elabz.com/arduino-shrunk-how-to-use-attiny13-with-arduino-ide/
Preparing the hardware: Datasheet: http://www.alldatasheet.com/datasheet-pdf/pdf/255658/ATMEL/ATTINY13A.html
I needed not much more then the powersupply and a 100nF Capacitor near the supply pins connected to gnd and vcc. http://forum.arduino.cc//index.php?topic=195395.msg1441864#msg1441864
ATtiny 44: Works!
Preparing the IDE: Should work with (Arduino-Tiny Cores) described in the link for ATtiny13 and the IDE^
I will write more about the other ATtinys and post pictures/sketches while going on trying them. I hope this topic could be useful for others trying to get these tinys to run with the arduino IDE.