Sigma 100-300 F4
Though not as fast as the 120-300 2.8, it works very well for outdoor sports (haven’t tried hurling though).
It is also much lighter and cheaper.
The wireless router doesn’t replace the modem, but gets gonnected to the modem (through the Ethernet port of the modem).
You will then need to take out the USB plg between the PC and the modem and connect the network port of the PC to the router (via a network cable).
In short, wall plug to NLT modem to Router to PC.
The laptop can then connect to the router wirelessly, the router dealing with the Internet access sharing.