Combining can be tricky. You have to make sure you know exactly what part you are working with so that it fits into the new rig. Check them well before you make the decision to use them in the new system. Now, I can give you a personal preference walkthrough for a new system and then you can just apply what I'm saying to old parts if you want to use them.

First, a good site to go to for parts is newegg.com. If you go to the specs section, you can make sure that what you are looking at matches the slot you are trying to put it in. Next, everyone has a favorite graphics card maker either AMD or NVIDIA. NVIDIA is a little more expensive, but the high end ones typically are a little more powerful, but as I said, you are going to pay for it. I am more comfortable with NVIDIA graphics and intel processors, so I will do a walkthrough with that.

First, pick a CPU. I7 (there are several, for minecraft it really doesnt matter) has 8 cores which meets that spec you wanted. Verify the slot type number on specs sheet.

Go to the mother board section and sort it by that slot type so you know all the boards you are looking at fit the CPU. Pick a board that supports USB 3.0, DDR3 1600 or better, and PCI 2 or 3.0 x16 (for the graphics card) and PCI express (fits your typical sound card but some are just PCI).

Go to Graphics cards and pick Desktop, then NVIDIA (as I said just my preference). Pick one in your price range. If you have high end games you play, research the spec for those to be played on mid and high detail so that you get one that supports your game. I would stay at or above GTX 400 to ensure new games play well or decently.

Pick a sound card. If you just listen with a couple of speakers, any generic one, like a low to midrange SoundBlaster card will do. If you do recording or have massive suround sound, Get a higher end card that has good reviews (reviews are a MUST on MB and soundcards as these 2 items have more crap than other components).

Buy and DDR3 1600 or better in your price range in the amount you want. I would stay at or above 8 for minecraft so that you can dedicate 3-4 gigs to it.

Hard drive: Solid state (SSD) if you can afford it for at least the operating system, will save you tons of time. loading things and on bootups. The more things on a SSD the faster each of those programs will be. If not, then get a 7200 RPM or better HD. I like the Western Digital 10k RPM velociraptor if building with HD and not SDD.

Google power supply calculator and determine what you need to run your machine. Add 1-200 to whatever it says to allow for expansion. If you can, get a case that has back access to hid the cables and help prevent air flow disruption. Modular power supplies help also since you can remove excess cables.

For cooling, unless you are doing dual graphics cards and overclocking, air is fine. I usually recommend upgrading the CPU fan because that part is REALLY expensive to replace and is usually higher in the case where there is more heat.

Odds and Ends: Don't forget to get paste for the CPU install or you will burn it out FAST. Make sure the case you pick comes with all the fans you want (and top air fans really help with heat). Just because it shows a hole doesn't mean there is a fan there. Dont forget your DVD/CD drive. Also, a nice add on is a SD reader which are usually pretty cheap. Get an steel case if you plan on moving it. I know that sounds crazy since it will be heavier than aluminum, but you wont rip it apart at the seams in transit, plus you can mod it better without ruining it. Before changing over, download ALL the most recent drivers for each part and put them on a thumb drive so you can update as soon as you finish all the initial installs. Dont forget the OS (and i have seen people get the upgrade version by mistake). Also BUY A GROUNDING LINE. It goes on your wrist and attaches to the case, keeps you from discharging static and ruining parts before you even use them.

I am sure I forgot to mention something, but I know others will catch it.

Most of it depends on your budget.
what are you working with?

So I assume maybe a budget gaming pc, mini itx build or something