What is the best 30-40pound graphics card for recording minecraft?

Well, it depends on what resolution you will play and record the game at. If you want to record it 1080p and get a decent frame rate (35-50 FPS), you'll have to buy something more expensive, like a GTX650 or an R7 250X which are both around 70-80 pounds, or even something a bit better if you can afford it. In any case, if you want to stick to your budget, you can get a GT630 (like mine) or an R7 240, which will run Minecraft at about 30-40 FPS, but while recording you-ll probably get around 20-25 FPS at best. So, for recording, you should probably look for something a bit better.