A quick update to this, I noticed that after starting the game up and selecting 'Play' I did not have this problem in 5 starts. I then tried to start by selecting the server through the browser and 4 out of 7 times both DayZ and Steam crashed (with no errors).
As per what Rebeliant said (thank you for the suggestions btw), I have updated Windows as well as my display and sound drivers. I then tried the game but it still crashed when selecting a server. I did not try to start repeatedly however.
I then reinstalled DayZ and tried to play. DayZ crashed on two (2) more occasions. Once more I did not try to start repeatedly.
After that I then reinstalled Steam and try again but I still had the same problem. I did not try repeatedly though.
I then tried to play by selecting the "Play" option and not try to manually select a server and I have not had DayZ or Steam crashing. I have only tried this about 4 or 5 times. I can also select other servers if I quit that game and select a server from the server browser screen as long as I don't exit the game back to Windows.
My time is limited today so I will keep trying this later. I will update this in a day or two.