In addition to what others have suggested, you will also need a decent set of speakers or headphones, unless you already have them. Drop the internal optical drive - you won't use it. You should add an external HDD to your budget to back up your PC.
There are a couple of areas where it is worth spending extra money. Firstly, there's the PSU. A bad PSU has the ability to destroy the components inside your PC so you want a decent one such as the ones recommended above. Secondly, there's the monitor. The monitor is your primary means of interacting with your PC. You want good graphics so don't get a cheap TN (Twisted Nit) monitor as these often are not true 8-bit colour per channel but dither 6 bits. You will want an IPS or VA monitor as these give much better pictures (but cost more). Don't go overboard, though, because once you discover how awesome PC gaming is you will want a better GPU and a better - higher resolution - monitor. (Don't worry: your PC will happily manage two monitors.)
If you are going to build the system yourself I would recommend against a Ryzen build simply because a BIOS update may be required and it can be very disheartening for someone like yourself to appear to have a non-functioning system and have to immediately return the motherboard to OCUK for that update. OCUK will happily build your PC for you for a very modest price and sort out any such issues during the build.
As already mentioned, AMD's Vega GPUs are imminent - 10 days - so waiting for reviews of those is a good idea. I have read that the Vega GPUs may be offered as bundles with money-off vouchers for Freesync monitors, so that will definitely be of interest.
There are a couple of areas where it is worth spending extra money. Firstly, there's the PSU. A bad PSU has the ability to destroy the components inside your PC so you want a decent one such as the ones recommended above. Secondly, there's the monitor. The monitor is your primary means of interacting with your PC. You want good graphics so don't get a cheap TN (Twisted Nit) monitor as these often are not true 8-bit colour per channel but dither 6 bits. You will want an IPS or VA monitor as these give much better pictures (but cost more). Don't go overboard, though, because once you discover how awesome PC gaming is you will want a better GPU and a better - higher resolution - monitor. (Don't worry: your PC will happily manage two monitors.)
If you are going to build the system yourself I would recommend against a Ryzen build simply because a BIOS update may be required and it can be very disheartening for someone like yourself to appear to have a non-functioning system and have to immediately return the motherboard to OCUK for that update. OCUK will happily build your PC for you for a very modest price and sort out any such issues during the build.
As already mentioned, AMD's Vega GPUs are imminent - 10 days - so waiting for reviews of those is a good idea. I have read that the Vega GPUs may be offered as bundles with money-off vouchers for Freesync monitors, so that will definitely be of interest.