AVR switch best practice
It doesn't really matter if you implement it as low or high active switch. However, since you need either a pull-up or pull-down resistor anyway (to have a defined logic level when the button/switch is open) it may be worth noting that the AVR controllers IO pins have a integrated pull-up resistor (of about 10k Ohm) that could be activated/used.


  If I am using the pin with HIGH value and by pushing the button it connected to groud, I saw some of the blogers put resistor before the button and connecting it to VCC:


That resistor actually acts a pull-up resistor. It is not necessary to limit the current from/to the IO port through the closed switch to GND, because it has a very high impedance when configured as an input. 


  what should be R1 value?


Since transmission speed and edge times and not an issue for something "slow" like pushing a button, the main consideration is to limit the current to a sensible value. With something around 50k Ohm you would limit the current to 0.1mA at 5V, which should be fine. You don't want a pull-up that is to "weak". Imagine using 1 Giga Ohm. That would essentially be the same as leaving the pull-up out and would not properly bias the input against the respective level.


  If I am setting the pin to LOW as default, should I use resistor as well, but connect it to GND?


Yes, that would be your pull-down resistor.