To get 125mbps actual bandwidth you will need something that can do 600mbps or better on a single band.
I have an ASUS RT-AC68P(R, U, W versions are just as good as the P), it is rock solid and I love it. It has 600mbps on 2.4 band and 1300 on 5ghz band. This router runs for $150-180 new.
The only one I would recommend for cheaper would be a TP link Archer C7 which is around $100.
ADDED:
My router can do actual 200-250 mbps to the intel 7260 wifi cards in my laptops.