Both AMD and Nvidia now bundle software for recording your gaming. You can also download other apps that do the same.
Minecraft is not that taxing so ~ £100 graphics cards are more than fine e.g. AMD RX560 or Nvidia GTX1050. Those would also be able to run Elite on lower settings.
If you have a budget around £150-£175 then a 4GB RX570 would more than meet your needs and your CPU shouldn’t have problems keeping up for 90% of games out there. An nvidia 1050Ti or 1060 would be the other option.
There are loads of flight sims available. For a gaming/dog-fighting one world-of-warplanes seems to have fans. I have not tried it, but it’s free (with paid for add ons).
[video]https://youtu.be/6HzRBOBHn4Y[/video]
If that’s too arcade like il-2 1946 would probably run on your current card and cost less than a tenner from gog.com and be a good intro into a proper ww2 sims (it has more recent successors).
If its fast jets DCS world is free for the base install with the more basic add ons quite reasonably priced (but I’d recommend one of the better GPU’s for that). Whilst it has got some simplified aircraft and missions it can still take a while to master and has some very realistic add ons that require a lot of effort to learn;
[video]https://youtu.be/GgfKVIife4U[/video]
EDIT – some people might question DCS for a 9 year old… however I got my 7 year old daughter to land an SU 27 on the Admiral Kutnetsoz with a few of the difficulty settings turned down. It was great fun 🙂