Yes it can work for wireless or wired internet. However if your talking about your lan network, most cases it needs to be wired, meaning that although your router has wireless internet, the router still needs to be physicall wired to the NAS via ethernet.

However there are some exceptions to this. I believe QNAP for example has a wireless adapter support, so you don't need to be physically wired to the router, and thus can operate wirelessly in your home lan network. You just plug in a wireless usb adapter of your choice into the QNAP usb port, and you will be able to connect.
Qnap opted for a wireless adapter approach.
http://www.qnap.com/en/?lang=en&sn=1014

Synology has a NAS product with the wireless feature internally built into it
http://www.pcworld.com/article/2018283/syn...ough-value.html
There is a lot of difference between low/mid/high end model NAS such as....

1. hardware specs e.g..... how much ram (more better), cpu power (higher for better performance, lower for the opposite, but has better power savings), network speed (the speed of how fast data uploads/downloads in your local network. This also affects streaming speed/quality for media such as music and hi-def videos).

2. software/firmware e.g. the graphics user interface navigating/configuring the options on the NAS. ease of use to install/modify apps. how many features it provides you to do, ranging from entertainment, utility, security etc etc.....

3. how much storage bays does it have, to support how many, and what types of hard drives. In summary, what is the max storage capacity can the NAS have ?

4. aesthethics - the outdoor appearance and build quality. Also is it a box or a rack chasis ?

5. warranty and support - is warranty covered ? And what is technical support like ? If you opt for a DIY NAS, nobody is going to help you period. But maybe a branded NAS has technical support on their forum to assist you regarding their product if you buy it.
*update

I found a low end ZFS NAS here
Review:
http://www.tweaktown.com/reviews/5130/info...iew/index3.html
http://www.eonnas.com/us/products/eonnas-p...-210#ad-image-0

http://www.amazon.com/Infortrend-EonNAS-2-...2/dp/B00BBPYTI2
http://www.marketwired.com/press-release/i...ies-1773398.htm
The thing though, it has only 2gb ram, so this could be problematic could stuff like deduplication which requires alot of ram, minimum 8gb ecc ram i heard :/ so i'm not sure how well a ZFS NAS would work when not provided enough ram it should have 

Also another thing, this particular brand lacks extra features that brands like Synology and QNAP offer e.g. torrent client etc.... But instead it focuses more on reliability of storage, which to me sounds good, seeing as thats mostly i want it for