In answer to your specific questions.
You may not be able to get that high on that chip. I have two of them, one goes to 4.2Ghz, and the other to 4.5 Ghz. However, the stock cooler worked well temperature-wise. My overclock was limited by voltage. If you want to save money, use the stock cooler, which is the same one supplied with the i7, and take what it gives. Even 4.6Ghz should be enough.
The MSI H81M-P33 is an appropriate budget motherboard.
If you can afford it, an i3 4170 on the stock cooler is probably a better choice in general, and the 3.7Ghz clock is decently fast.
There is another alternative, although you will need to check on availability. The Athlon X4 860K is a decent budget CPU.
Here are some possibilities.
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($66.88 @ OutletPC)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.50 @ Newegg)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($45.75 @ OutletPC)
Total: $147.13
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-02-27 05:34 EST-0500
i3
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel Core i3-4170 3.7GHz Dual-Core Processor ($114.89 @ OutletPC)
Motherboard: MSI H81M-P33 Micro ATX LGA1150 Motherboard ($45.75 @ OutletPC)
Total: $160.64
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-02-27 05:35 EST-0500
Athlon X4 860K
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($72.89 @ OutletPC)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.50 @ Newegg)
Motherboard: ASRock FM2A88M PRO3+ Micro ATX FM2+ Motherboard ($52.38 @ Newegg)
Total: $159.77
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-02-27 05:36 EST-0500
FX6300
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD FX-6300 3.5GHz 6-Core Processor ($105.98 @ Newegg)
CPU Cooler: CRYORIG H7 49.0 CFM CPU Cooler ($34.50 @ Newegg)
Motherboard: Gigabyte GA-970A-UD3P ATX AM3+ Motherboard ($61.98 @ Newegg)
Total: $191.46
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-02-27 05:38 EST-0500
In the FX6300 build, the motherboard has been selected so that a FX8350 upgrade would be possible in the future. you could save $10 if you forgo this possibility.
I know you say CS:GO only today, but I would use something other than the G3258 to give you more flexibility if you cange your mind.
If you are outside the uS, link us to a site which you might buy from so we can fine tune the parts.
Get a good PSU, cut corners elsewhere. A good PSU will last for many years and through several builds and will support substantial upgrades.
It is assumed that all but the i3 will be overclocked to some extent, and the two AMD chips need a substantial overclock for the best results.