Mine is wired. It uses two 'D' cells. I intended to fit a mains PSU - probably a switch mode one - if replacing the 'D' cells proved expensive, but they've been there for some years now. About a month ago I had to remove it to do some redecorating and checked the voltage while I was at it. 1.4V. They'll last a few years yet, so a mains powered one isn't going to happen.
My bell-push is an old fashioned brass one with the word 'Push' on the button - as if anyone would try to pull it! I would steer clear of the illuminated ones that have a clip on plastic cover. They tend to get nicked by less scrupulous citizens who find they are unavailable unless you buy the whole shebang at vast cost. Also you really need mains power for one for those. Batteries wouldn't last any time!
I don't recall paying a lot of money for it. I think I got it from Homebase or B&Q