Which of these is the best CPU cooler for me?

[Nintrex]

I am new to building computers, and when I built my first computer I went with the stock CPU cooler with the intention of upgrading it later, which is what I'm doing now. However, mainly due to my inexperience and various other factors I've more or less been running around in circles for the last week, I've finally narrowed it down to three choices and am looking for someone to give me a simple answer for which is the best choice.

My computers Specs are:

Intel core i5-4570 3.2 GHz CPU
MSI Z87-G43 Motherboard
WD 1TB HDD
ASUS GTX760 VGA card
8GB DDR3 RAM
Coolermaster 750 Watt PSU
Thermaltake Commander MS-III mid tower case (limits CPU cooler height to 155mm)

the three coolers are;

Cooler Master Hyper TX3
Cooler Master Hyper T4
Thermalright True spirit 120M

I'm honestly not sure what the difference is between the two cooler masters besides price and all the reviews I found for the thermalright that actually mentioned specs specifically mentioned an i7 CPU and one said that the installation required the removal of the motherboard and thus is a lot of work for an upgrade job, so if that's your recommendation could you please clear that up.

I am also open to recommendations other then the three listed above, price is not an issue but the height limit is (155mm/6.1In).

some details that might help:
I intend to use this computer for gaming
I intend to use the optimal settings when gaming
I intend for my gaming sessions to only be a couple of hours at a time (2-3 hours max)
I do not intend to do any overclocking in this build

Thank you in advance for your help

 

[ksham]

The CPU isn't overclockable so you don't need an aftermarket CPU cooler. But if you want, get whichever one you want.

 

[bryonhowley]

If you are not going to overclock the only real reason to get a after market cooler then would be to get one that is quieter than the stock cooler.

Personally for a air cooled solution I still like the Cooler Master Hyper 212 EVO.

 

[Xondat]

With the TX3 you will have a much quieter system; I've used it for 3 years running 5-6 hours per session and it's kept at a low temperature for a 92mm fan cooler and it's also quiet. The only two reasons you should be upgrading your cooler would be for a quieter system and for lower temperatures.

 

[Calculatron]

The TX3 has three 6mm heatpipes, has the smallest stature, and utilizes a 92mm fan.

The T4 has four 6mm heatpipes, medium stature, and uses a 120mm fan.

The Thermalright True Spirit 120M uses a 120mm fan, but has a small stature. It'll cost the most, but is the highest quality solution. Here is a link to the installation guide: http://www.thermalright.com/installation/TS-120M/TS-120M%20Installation.pdf

The overall basic is that you will have to remove your stock cooler, and the stock backplate that keeps it mounted to the CPU and motherboard, and then install the mount provided. Once you have the mount installed, you apply a touch of thermal compound, then carefully install the heatsink.

Your case is semi-new, thankfully, so you will not have to remove your motherboard to install a new cooler. The backplate that your motherboard is mounted to has a cut-out specifically for the ease-of-installation of aftermarket coolers. It's pretty big too: http://www.xbitlabs.com/cms/include/image.php?src=/images/cases/thermaltake-system-cases-review/p59.jpg&width=350&height=307&cache=1&quality=100&aspect=0&format=