in terms of insurance then don't tell the insurance company you have an alarm as its bells only and self maintained.
insurance companies can be very general or very specific as to what you must have and chances are you wont save much if anything on insurance quotes in your case
some companies wont be over keen, but reality is the min panel battery will need to be replaced every 3-5 years and it should be tested at a service to check it is likely to be okay for another 12 months although modern panels will tell you when its getting very low. How long they actually last varies.
no wireless means you dont have wireless signal or batteries to worry about.
as for how you want to be notified, apps are okay, but relay on the coms board fitted, so WIFI or GPRS seem to be the boards available for pyronix.
Dont see a phone call or sms message available. the app does require a subscription as would the gprs connection.
Texecom, again is a similar situation. No charge currently to use app, unless on 4G.
Orisec there's a bit more flexibility but options depend on the panel, in terms of coms and what those coms can do currently no charge for the app, you can use your own sim card so you have a little more flexibility on whats paid potentially
I would be surprised if an installer will give you all the options available so you need to make it clear what you want and you can view all the manufactures sites and read up on what things can do.
Cant comment on prices you have been offered as dont know what you have been offered.
For example Orisec have numerous keypads and several different variants of the CP20.
Texecom have various keypads, Pryonix from memory have a few less options on what keypads are available.
All the panels should be able to accept existing sensors and bellbox and the speaker if 16 ohms, don't know the condition of what you have but would guess its dated but maybe functional, but in some homes this gear still looks brand new and in other can look like its had a rough life.