Orion, it's not the case that an exact specification can be recommended for your list above.
Speed of the machine's response depends on a variety of factors, like CPU/s speed, amount and speed of RAM, make and model of motherboard etc. The speed you get will likely be determined by the speed you need, but also the budget you have. Amount of hard disk space etc is something others can't decide for you. You'd need to work out how much of space you need.
Question is - do you even need a your own server? What makes you think you do?