Best way to record gameplay for short clips?

[PardonTheSuit]

Hello everybody! So today I was playing a game of Battlefield 4 and I was playing as a sniper, and I landed a really amazing shot. I was lying prone on the ground and was looking around when a helicopter is directly in front of me. When this happens, I have the instinct to try and shoot the pilot with my gun (because the majority of the time I'm screwed when a helicopter flies above me). I mainly go with either the assault or the engineer class, so being a sniper is something that is very new to me. I decide that I might as well try and shoot at it, so I shoot where I think the pilot would be in the helicopter. I ended up shooting him in the head and killing him, causing the helicopter to crash. While I was very surprised that I made this shot, I immediately thought to myself "I wish I had gotten that on video!". I wish that I had recorded it because 1.) I could rewatch it if I wanted to, and 2.) I would have legitimate proof that I had made the shot, which in my case, I don't have any proof and I never will.
So my question is, is there a way that I could record my gameplay for that purpose (just record it while playing, and if something cool happens like that, I could just save the clip). I wouldn't intend on live streaming or anything like that. Maybe something that wouldn't impact my performance as much (preferably not software), I think that I would be looking for maybe a cheap capture card? I'm not really sure, so it would really help if I got a response. Thank you!

[Bad 💀 Motha]

BandiCam
MSI Afterburner
OBS Studio
Geforce Experience

[MaddDoktor [Linux]]

I have just recently started to try to record gameplay with OBS in Linux, but maybe my 7 year old PC is not quite up to the task. With old i5 650 3.2 GH, 8 GB RAM, GTX 1060 (PCIe 2.0 slot), mSATA SSD in SATA adapter on SATA2 port, 720p gameplay is still over 60 fps and recording is smooth at 30 fps. But my setup is not quite up to recording 1080p, which slows gameplay even at medium game settings and drops so many frames in the recording to the point that it is not pleasant to watch. There is another Linux program called SimpleScreenRecorder that might be faster. An i7 would likely help.

But I may just look for an external HDMI recording device that can record independent of the computer to SD or USB flash memory or hard drive. That way it will not slow up gameplay at all, and at around $100 more or less, is cheaper than buying a new computer. I just haven't figure out what the best one is yet. Make sure that it supports either NTFS or exFAT filesystem, because FAT32 is limited to 4 GB max file size and I have heard of some HDMI recorders that chop video files into even smaller sizes that you need to stitch together.

PS: I just tried SimpleScreenRecorder in Linux with a setting that does not try to compress the video on the fly, and that works great recording TF2 in high settings @ 1080p 30 fps, while the game is still over 60 fps most of the time. File size is much larger, but if I want to save something I can post process it for more compression. I should see what other file types OBS has instead of trying to compress it to mp4 on the fly.