Depends what your actual broadband speed is now. You need to test it with a PC or laptop wired directly to the router, wireless will give a false reading as it's limited by the wireless speed. If you're on ADSL 2 I think the max is 24MB,which is plenty for your use case. Depends almost entirely on your distance from the exchange though.
Fibre is definitely worth the extra if you have multiple devices in simultaneous use and your wired speed is under 10MB or so. We got it because standard ADSL only gave 1MB and with 5 in the house we needed the bandwidth. Now we have 36MB and no issues.
Bear in mind also that the max wireless bandwidth over 802.11g is 56Mbytes or about 6MB and it's shared across all devices. We have a second WiFi access point (a reconfigured router) for this reason, the kids have one and we have the other.