Adding 10KW capacity to existing house
Your house already has all those circuits. Look at your breaker panel at all the single-space (1 pole) breakers. Almost all of them are 15 or 20 amps.  A 20A breaker can drive 1920 watts on a continuous load.  A 15A breaker can carry 1440W on a continuous load.  Worst case, at 1200W per circuit, you'll need eight 120V circuits, and your house will have that.  

You are saying 1200W but that is just a common nameplate rating on a PC power supply. You can buy a "Kill-a-Watt" power meter and measure the actual load when the server is at max performance.  Read the VA number and use that in place of watts.  For instance if the server reports 900 VA actual, you can put two on a 20A circuit.  

Your kitchen has two of the 20A jobs. Your garage probably has another 20A.  They're all over the house. 

If you don't know what breakers serve what receptacles, get some night lights at the dollar store and plug em in all over the place. Then turn on one breaker at a time and walk around and see what lights up.   You can turn on several breakers at a time or even half the panel, and then you can make a logic game of it.** Things which DO light up are on that circuit.  Things which DO NOT light up are on a different circuit.  Feel free to cover your receptacles with Post-its. 

Crowding all that equipment into the garage, and paying a guy to run a bunch of cable, is silly.  Not least, the garage location will require GFCI breakers since this will be new work. 

Also by putting it in the house proper, your A/C units will come to bear.

** if you have &lt;32 breakers,  you should be able to match up every outlet in five loops through the house.  Print out a bunch of sheets of paper with the numbers 1-32 on them.  First you set odd breakers on, and loop through the house. Strike out (exclude) even numbers if it's on, or odd numbers if it's off. Next turn on every other pair: 1-2, 5-6, 9-10 etc. and cross out the circuits the outlet can't be.  Then every other group of four: 1-4, 9-12, etc. Two more rounds, and each sheet of paper will have only one number remaining.