Spec in the OP sounds a good price. Built a budget gaming PC for T junior a few months ago, Skylake i3, GTX750Ti, 240Gb SSD, 8Gb DDR4 just under £400 (add £100 for OS). He says it is plenty good enough for him playing mainstream FP games. His only complaint is now wanting a bigger HD. Will be adding a normal 2Tb HDD, 7200rpm if he’s lucky.
An i5 and better GF Card as specced would be next level and easily play popular games. Although while the i5 has more cores which is good for multitasking, for games tests like these don’t show a significant difference. Could be GF card bottleneck? Of course CPUs and GPUs can be upgraded later with the right sockets, for that reason I would stick to Skylake. Some previous gens offer value but you have to do some research then weigh up pros and cons.
Steam machines like the Alienware ones are an alternative but a PC is more flexible for homework and general PC skills.