Upgrading Router

[#1]

Hello.
New fibre customer here. Very happy so far, paying for 76mb getting a full 80 down 20 up wired.
I was hoping to upgrade the router to see that speed over wireless. Is it possible to see those speeds over wireless with an upgraded router?
I've got a sagem router and open reach modem.
Do I need a certain type of router for fibre to work? Vdsl? Or does all the internet 'stuff' happen in the modem and the router is just giving me Ethernet ports and wifi?
Thanks
P.s any recommendations on an upgraded routers?

[#2]

If you get one that supports PPP over Ethernet (PPPoE) then you can continue to use the Openreach modem that you already have. Alternatively you could buy one with an integrated VDSL modem and then you could simplify down to one device instead of two
Personally I'm currently using the supplied Openreach modem with an old trusty D-Link DIR-655 that I've brought out of retirement now that I no longer live in a Virgin-cabled area. I believe that I could get the full 80/20 speeds over wireless with this router, but a) none of my devices have got fast enough wireless themselves and b) I'm only on the 40/20 product