Well, I would definitely go with wireless headset if you have a pet. My dog killed my Turtlebeach PX21 in 3 days, by biting the cords, and the few disadvantages of wireless are okay when your pet cant destroy it. Also if you don't have much desk space, wireless is for you.
If you are going wireless, get the Afterglow Wireless Headset (
https://ebgames.com.au/ps3-159391-Afterglow-Wireless-Headset-PlayStation-3)
I have had this one and you definitely get quality for money. You should be able to get it shipped pretty easy, this is just Australia's alternative of Gamestop, run by the same company.
I enjoy using this and just walking and making lunch while listening to tutorials or music. Because of the 100ft range, I can walk up and down the length of my house (my house is very long) and just manage to hear it.
Make sure however you get a chargeable one, and not a battery powered one. One disadvantage I have found is charging it, as even though it has a 10 hour battery life, gaming all day can be difficult, causing me to get up and actually walk around, acknowledge my pets and family, etc. (yuck)
If you go wired, the Turtlebeach PX21 is really nice, for the three days I had it, although the cords are quite flimsy, i did manage to repair it with electrical tape however. The headset is comfortable, and the microphone works very well, but picks up a bit of background noise, especially a clicky clacky keyboard.
If you are looking for something more expensive, get the Turtlebeach XP seven, its very comfortable and is designed for gaming. The amount of different setting you find on this device, along with other Turtlebeach headsets is amazing, and the quality is just as good. The surround sound on this is godlike, with the sound giving you a full 360 degree perspective.
So yeah, hope this helps.