Hello
@ItsMeS.C, you might want to check out my other thread, where I describe my new PC (as well as some issues with building it):
https://www.overclockers.co.uk/forums/threads/my-first-built-pc.18914645/
Basing on your boyfriend's games it will be okay to copy the build (except for graphics, cyberpunk can be needy and I would recommend a 6-8GB graphics card instead of a 4GB).
Here's what your shopping list could look like:
-Gigabyte B450M DS3H motherboard; ~£60
-HX430C15PB3K2/32 RAM (HyperX Predator 3000Mhz, DDR4, 2x16GB); ~£130 (32GB of RAM total, I can assure you this will be way more than enough, a majority of games will never reach half usage of that value)
-AMD Ryzen 7 2700X processor; ~£150 (you could also go for AMD Ryzen 9 models, most of them will work with this motherboard but they will be significantly more expensive than 7s)
-Palit GeForce GTX 1050 Ti StormX 4GB GDDR5 graphics card; ~£150 (exact model is optional, if your boyfriend plays Cyberpunk, you may need to get him a stronger card, a 6 or 8 GB one, but the prices on those can be scary)
-TX550M power supply; ~£70 (if you decide to change any items from this list, you may want to check exactly how much power the PC will need, but 550W should be enough for your build)
-WDS500G2B0C SSD (500GB); ~£60 (an SSD drive, much faster than HDD - the more space on it, the better. 500GB is not a killer if your boyfriend wants to install his games on this drive)
-Additional HDD drives if he needs more storage space (they are slower and tend to be more faulty than SSD drives, but are much cheaper, so ideally you would want an SSD for system files and a HDD for storage.) Depending on how much storage he needs, I would consider getting at least 2TB - prices vary, depending on your choice.
Also worth pointing out that he will most likely move the drives from the old PC, so you actually may not need any new ones.
Total build cost: around £620 (if you do it yourself), not including extra HDD, new case, system, wireless card and cooling systems.
It is very important, if you decide to change any item(s) on this list, you will need to make sure the parts can work together. You can usually find this information on the motherboard manufacturer's website.
-A standard case can be reused or bought for £30-60; (it's just a box to hold the parts afterall, unless you are after some special features, such as cool-looking LED lights or built-in camera memory card readers etc.)
-Depending on system licence you probably could install the 'old' system on a new PC - but you can get Windows 10 Home for around £20 if you look online;
-Wireless card is optional - you will not need it if the computer has wire connection with your router. If you want to go wireless, you will either need a card (you will plug it into the motherboard) or an adapter (USB stick). Depending on what you decide to get, £15-50;
-Cooling system - can't really give you any advice here, the default cooling is always air (built-in fans) and each part that needs cooling will come with its own fan(s). Proper cooling will extend the life and improve performance, but I never had any issues with air cooling (over 13 years on one PC, not a single part malfunctioned due to heat damage/excessive use).
This list offers you a budget gaming PC with very decent performance - not many games will require better specs. If you want a similar pre-built PC, you're looking at £1200-1500, depending on the store, as far as I noticed they all tend to overcharge a 'little' - if you are not sure you or your boyfriend can assemble the computer, you may always bring it to a repair point and they will assemble it for you, you will end up saving about 30-40% of the price this way compared to a pre-built PC.
All the information about what-goes-where can be found here
https://www.gigabyte.com/uk/Motherboard/B450M-DS3H-rev-10#kf but this will only work for this motherboard (you will need to find a similar page on the model you decide to get).
Also worth pointing out, that if he has a 7-year old PC now, the upgrade will be significant (and I mean it, 'average' parts available 7 years ago are considered crappy nowadays).
This PC will provide very good gaming experience and will allow your boyfriend to fully enjoy the games you listed, but as you mentioned your budget is £2000, so you may want to look for an even better setup.
All listed prices are for new parts.