The GTX 770 is slightly faster than the R9 280X, so if (through sales, rebates, etc.) you can find the 770 cheaper or the same price as the 280X, go with that. Otherwise the R9 280X is probably a better purchase.
Hard to say on the motherboard without knowing what your expectations are. £150 will get you a relatively high-end motherboard, where the differentiating features will be the number of PCI-E lanes for SLI/Crossfire, built-in Wifi/Bluetooth support, great overclocking hardware, etc. If you don't need any of that, I'd just recommend spending less. What do you need it to have?