Purchased a 8320e + AsRock Fatality FX99 = $159 back in December at Micro Center. Added 16GB RAM G.Skill Overclockable DDR3 RAM for $79 CAD and a 250GB Samsung 850 Evo for $69. Reused old dual fan Coolermaster Hyper 212 and it's happily running at 4.5Ghz at 1.35 volts in a $40.00 Corsair Carbide Series SPEC-01 RED LED Black ATX Mid Tower Gaming Computer Case. Added a lightly used Asus Geforce 750Ti I got for $75 along with a $20.00 used Corsair CX500 and built an entire decent 1080P gaming / encoding / rendering, developer, VMWare server for under $500 in total.
Sure you could go with a $130 Core i3-6100 + $100+ Z170 + %~20.00 more expensive RAM and build a similar computer that may be slightly better in some specific games but then when you add up an entire budget build you can see where you could spend the $100.00 difference on a much more capable video card or another 250GB SSD for a 500GB Raid stripe.
This is where I think the argument for the not-guaranteed to overclock very welll, locked processor with an unusable GPU with the possibility to be disabled by an Intel "McUpdate". These unbalanced i3-6100 / Z170 combo falls apart unless you plan on wasting $130.00 now on a processor and finding out it can't handle newer multithreaded games that well (console engine development continue to take advantage of multi-cores, especially with the 7th core being unlocked on both PS4 and Xbox One to be used to speed up gaming) and then in a year likely having to sell anyway for a Core i5/17 to get the desired speeds you wanted in the first place.
If the i3-6100 was a little cheaper and you could pair it with a much cheaper H81 and still get away with Bclock overclocking it would be more attractive but you lose the APU capabilities of the CPU (you're losing something you're paying for) but you're forced into buying Intel's highest end chipset / motherboards to gain bclock overclocking.
The unlocked FX8320e + FX97/99 AMD solutions just make more sense if you're on a budget. You can build a much more balanced PC for the same or less money and you still get a very feature rich motherboard.
Just my 2 cents.
As for the OP, you do want to overclock your CPU. Each FX CPU is unlocked and has a some free performance on tap. You can get away with a simple $15.00 aftermarket cooler
http://www.newegg.com/Product/Product.aspx?Item=N82E16835103182 that will allow you to reach roughly 4.2/4.3Ghz without much effort or voltage increase. These specific coolers have very quiet fans compared to stock so they're worth changing for even if you don't plan on overclocking. The 8350 is already pretty fast out of the gate but this cooler will make a pretty dramatic difference in acoustics and performance for a small investment. I still recommend grabbing a higher end Noctua Heatsink/Fan if you can afford it as they're top notch and offer amazing warranties and give you free bracket upgrades when new sockets come out but that adds to the total cost.
Anyway, get at least a $15.00 cooler (or grab a quality Noctua) and overclock that CPU to 4.3Ghz (4.5 or higher on an 8350 with a good Noctua is pretty reasonable) Ignore the "you should have bought X because Y" arguments. You already have a decent processor that will likely age better than any Core i3 series processor.
If you're dead set on water cooling grab at least a Corsair H60 (the cheaper CLC are pretty garbage quality wise or very loud) but I recommend the H105 for the 8350 if your case can accommodate the thickness of the radiator as its a little smaller and easier to mount and cheaper to find replacement fans for (120mm vs 140) and I believe cools the same or better than the 110 series, plus it's normally a little cheaper).
Good luck.