Electronic – arduino – Reset pin on ATtiny84/85/2313 clarification

Atmel AVR042: AVR Hardware Design Considerations tell us that the capacitor on the reset pin is not necessary. Personally I think it's overkill. There is no reason for you to continue making dozens of AVR circuits, each and every one with that redundant capacitor.

As for the reset pullup resistor:

The reset line has an internal pull-up resistor, but if the environment is noisy it can be insufficient and reset can therefore occur sporadically. Refer to datasheet for value of pull-up resistor on specific devices. Connecting the RESET so that it is possible to enter both high-voltage programming and ordinary low level reset can be achieved by applying a pull-up resistor to the RESET line. This pull-up resistor makes sure that reset does not go low unintended. The pull-up resistor can in theory be of any size, but if the Atmel®AVR® should be programmed from e.g. STK500/AVRISP the pull-up should not be so strong that the programmer cannot activate RESET by draw the RESET line low. The recommended pull-up resistor is 4.7kΩ or larger when using STK500 for programming. For debugWIRE to function properly, the pull-up must not be smaller than 10kΩ.

If you take a look at professional products that incorporate the AVR micros, such as the Arduino, its numerous clones, dozens of dev kits, you'll find that most use a 4.7kΩ or 10kΩ resistor.

And particularily for your ATtiny13, its datasheet specifies that the pullup should ideally range [20kΩ, 80kΩ].

PeterVH provides all the info needed to use the Arduino Leonardo as an ISP with the arduino ide (version 1.0.1):

ArduinoISP on the Leonardo