Compatibility.. its a simple thing when it comes to PC.. Here are the things you would want to keep in mind..
1. Decide upon which CPU you want first..AMD CPUs need more power, they run at higher clocks, put out more heat, have 1 thread per core, not so expensive..intel ones are more efficient, take less power, run at slightly lower clocks, have 2 threads per core..2 threads per core=1.25x the performance..but they are expensive..
2. Lookup what socket is that CPU compatible with.. e.g., AMD FX8320 requires socket AM3+, intel 5960x requires socket LGA2011-v3, etc.
3. Look for a motherboard that has this socket to take the processor you are about to buy..
4. Now you will probably find a range of motherboards that support your processor..now you check what kind of RAM you need, the speed, class of memory modules you want to use.. currently boards made for AMD CPUs support only DDR3 modules AFAIK..If you want to use DDR4 look for a motherboard that supports it..AFAIK only motherboards with x99 chipset support
5. Chipset: This is all about features you want your board to support..some may have onboard wifi 802.11 ac support and some may not, some may have more number of USB 3.0 ports, some may have more number of sata III 6GB/s ports to plug in your drives..
6. Graphics card: As long as your motherboard has required number of PCIe slots, you are fine to select whichever card you want..'the only thing you wanna keep in mind is the graphics car's power consumption- to calculate what your PC's total power requirement would be..
7. Hard drive: I would always choose an SSD like 180GB or 256GB to install the OS, and a 2 or 4TB 7200rpm or 10000rpm HDD for bulk storage..that way you wont compromise on speed as u are having ur OS on an SSD and you dont have to shell out a lotta money to store ur data as u are using cheap still fast enough memory..
8. RAM: The modern boards support DDR3 or DDR4 modules and no board supports both of them..DDR4s are little bit faster, more power efficient, but damn expensive..for all gaming purposes, DDR3 modules with 1600MHz or higher speed is sufficient.. 16GB would be ideal to start with..
9. Power supply: You have lot of websites, which give you the peak power consumption of your PC if you key in your components..just find out what it your config's max power requirement would be.. ideal would be to buy a power supply with a wattage which is around 30% more than the peak wattage of your PC..this is to allow for minor upgrades you would want to do in the future and to allow for the errors in calculation of power consumption and power loss in a PSU..e.g., if my peak power consumption is 450W, i would buy a 650 or a 750W power supply..corsair makes very good ones..
I would go with a fully modular power supply like corsair AX760i..fully modular means you can connect the cables that you actually need and save some space..it makes cable management inside the case easy..so cooling the system becomes easier..
10. Case: For starters, I would advice cooler master haf 912..or if you can find a case with these features, you can go with it..
-mid tower case that supports ATX form factor(ATX, mATX, mini-ITX, EATX are all different sizes of motherboards)
-PSU slot at the bottom
-at least 4 120mm fan slots
-at least half an inch space behing the motherboard tray to manage cables..
a better case than CM haf 912 would be fractal design define r5..best ATX mid tower case I have ever seen..
11.CPU cooler(optional): They replace stock CPU heatsink and fan assembly with a better more efficient one, that produces less noise(especially AMD's stock cooler is very whiney, noisy.. there are both air and liquid coolers available.. for starters cooler master tx3 is a good choice..never buy an air cooler which costs more than $35..