I'm currently with Talktalk who also provided the wifi router. Would I find the information you suggested in the router or ask my provider?
The info should be in the modem.. if you go to the setup just see what kind of authentication is used.. I am not used to the model so I do not know the exact page on the setup to find it.. but there should be a user manual and about half the content is usually the setup basics.
Or just ring and ask the ISP .. depending on how painful it is to get through to their support department.. because you will need help to bridge the modem I suspect.
I would follow the line of least resistence.. since you cannot ever get rid of the modem.. you may as well use it as is.. and just bridge the new AE which is easy.
Open the airport utility and click on the AE icon, then click edit on the summary that pops up.
Go to the network tab and choose the option, off bridge mode.
Just leave the wireless as is.. it doesn't matter if you have wireless from both routers.. indeed since the bridge mode on the AE turns off guest network, just use the main router for guest wireless access.. but use your AE for all your wireless devices.