First off: The processor has little to nothing to do with your gameplay. Most standard processors from within the last three years will be able to EASILY run an instan ce of Minecraft. I have an old i5 from 2010 that can run Minecraft at 25% CPU usage - I could easily run three instances of Minecraft without having to worry about any sort of lag as a result of the processor. I currently have an i7 right now, and let me tell you, buying it for Minecraft, and at that, for any gaming, was a huge waste of money - an i5 could have done the job just as efficiently at a far lower price.
Notice - they both get around the same FPS (the i5 actually gets a bit higher overall, but that's for reasons unrelated to the graphics card and processor).
Another concern you might have would be RAM, and justly so, as RAM does have some sort of significance when it comes to gaming. Games and applications allocate your RAM as they process throughout time, so having a high quantity of RAM (quality is good too, but for now, the best you can normally get is the standard DDR3 RAM) helps in the sense that it prevents the application from totally freezing up. Running a game with an inadequate amount of RAM is not fun - you'll lose major FPS, the game will slow down in loading, there will be a lag between input and output and (at worst) your game may crash and/or freeze up. So, how much RAM is good enough to run Minecraft? Technically, 4GB will get you over the hill. How much RAM is good enough to do gaming? 6GB. You'll have more than enough space to run every game (and multiple instances of any game, at that). Anyone who says that 8GB+ is necessary to have a "gaming computer" is a flat out liar or has an inordinate amount of money to blow - you can run all you need on 6GB or 4GB (at worst). If you have to cap your RAM purchase, cap it at 8GB, but always be on the look out for computers that have additional slots for extra memory (e.g. laptop comes with 8GB but can be extended to 16GB). This allows you to keep your computer up to date with whatever you need (today we don't need 8GB, but in two years, I might be eating my own words).
Now, the hard drive. Doesn't really matter*. The amount of space it has is dependent on your ability to manage said space. Little to no effect on performance. Some may argue that the RPM of the hard drive (5400 RPM, 7200 RPM, 10k+ RPM, SSD, etc) has a noticeable effect on performance. The only area that a hard drive speed can actually effect (in gaming) is your boot up speed (for said application, rarely) and then your loading times.
*note - A hard drive does matter for those of you who record in game, but that's a different story.
Finally, the graphics processor. I've saved the best for last. The graphics processor is, HANDS DOWN, the MOST IMPORTANT THING YOU CAN BUY FOR ANY GAMING. Graphics processors are key to getting a high FPS in any game, period. In Minecraft, you might be able to get away with an integrated (as I did during Alpha+Beta with my old laptop) as it isn't too demanding, but for high quality, high fps filming and general gameplay, getting a discrete graphics card is key. Spend as much of your budget as you can on your graphics card, for it is THIS one piece that will get you the greatest return for all of your money. Additionally, get as much RAM as possible with your graphics card. Both quality and quantity are important in this area - aim for 2GB of DDR5, if not 4GB. Any graphics card listed with "shared RAM" is a graphics card that simply leaches off of your main RAM and thus are both slower and have less RAM to access, as a general rule. Try to avoid these.
Hope this helps!
