Wireless alarms are not considered to be as good, and the trade sneers as them.
However they are very easy for a DIYer to fit. I put one in my old mum's house and it took me a couple of hours, using just a cordless drill and a screwdriver, and reading the instructions carefully.
Ironmongery Direct has the top of the range Yale system on special offer this week at £135, it usually costs about £200. This is the one that phones three numbers in the event of an alarm and plays your recorded address. You can buy additional sensors if you have a larger house.
It is an advantage to have an extra keypad near the front door, or use a keyfob button, so the panel can be concealed well away from any likely point of entry, to stop anyone interfering with it before it has had time to raise the alarm. Once the siren has started to sound, attacking the panel won't stop it.
IMO if you are paying a professional to fit an alarm, you're better off with a wired one, but having it able to phone out is a valuable feature.
Insurance companies might only recognise more expensive alarms fitted to commercial standards by an approved company, with a maintenance contract. This is much more expensive. If you notify them of an alarm and they give you a discount, they might refuse to pay out if it was not turned on when you were burgled.
I am bemused at the idea of an insurance co failing to pay out because they were not notified that an alarm had been fitted, and would want to see evidence before I believed it (sorry).