Sorry about the response time, I've been dealing with a serious injury in the family and things can be unpredictable.
Anyway, the H5 Ultimate does cool better than the H7 but it may hang over the RAM. The H5 Universal is supposed to prevent that with a thinner weaker fan.
From what I have seen, the Fuma may cool a little bit better than the H5 Ultimate but is louder at the same percent fan speed (Fuma does have 2 fans vs 1 on H5).
Also reviews mentioned the Fuma can be tricky to mount, and easy to over tighten which can crush/destroy a CPU (especially Skylake which has a thinner PCB)
Most reviews liked the mounting system on the H5 Ultimate. If this is your first time it may be an important consideration.
The Fuma is also likely to hang over the RAM, but any of these coolers should be fine on a MATX board with a GTX1070 or other GPU. However, if we go back to the RAM I had first picked, the Corsair LPX, it's only 2mm higher than standard RAM and should fit under these bigger coolers even if they sit over the top.
Being a warmer climate I'd say go for at least the H7, but the Fuma or H5 Ultimate are even cooler options. The H5 Universal wasn't that much better than the H7 because it has a thinner weaker fan (although the heatsink is bigger). With the lower profile RAM any of these options should fit even on a MATX board.
One thing to consider with the larger coolers is the case width/size. Especially if you decide to go with a MATX board and a small case, though there are options that will work. The H7 is 145mm tall, the FUMA is 150mm and the H5 is 160-168mm tall. There are places that list the max cooler height (example:
http://www.toptengamer.com/pc-case-compatible-cooler-gpu-heatsink/ ) or you can usually find the info with an internet search of the specific case you're looking at.
If you're interested in the smaller MATX boards it looks like the two best options right now are:
$107 ASRock Z170M-Extreme4
http://www.newegg.com/Product/Product.aspx?item=N82E16813157675
Advantage for the ASRock is the Intel NIC (vs Killer) and lower price
$130 Gigabyte Z170MX-Gaming5
http://www.newegg.com/Product/Product.aspx?item=N82E16813128844
Advantage for the Gigabyte is board layout, M.2 above GPU not under it. Also reinforced PCIe slots
The Corsair LPX 3000MHz RAM is on the qualified list for the Gigabyte board, and should also work in the ASRock (similar but not identical kits are qualified)
http://www.newegg.com/Product/Product.aspx?Item=N82E16820233852
Here's a build with the H5 Ultimate, LPX RAM, and the Gigabyte MOBO:
PCPartPicker part list:
http://pcpartpicker.com/list/W7CbLD
Price breakdown by merchant:
http://pcpartpicker.com/list/W7CbLD/by_merchant/
CPU: Intel Core i5-6600K 3.5GHz Quad-Core Processor ($227.99 @ SuperBiiz)
CPU Cooler: CRYORIG H5 Ultimate 76.0 CFM CPU Cooler ($46.99 @ Newegg)
Motherboard: Gigabyte GA-Z170MX-Gaming 5 Micro ATX LGA1151 Motherboard ($135.66 @ Newegg)
Memory: Corsair Vengeance LPX 16GB (2 x 8GB) DDR4-3000 Memory ($79.99 @ Newegg)
Storage: PNY CS2211 480GB 2.5" Solid State Drive ($139.99 @ Best Buy)
Power Supply: SeaSonic G 550W 80+ Gold Certified Semi-Modular ATX Power Supply ($78.98 @ NCIX US)
Total: $709.60
You could choose the Fuma cooler, it's about the same price as the H5, or save about $10 by going with the H7.
If you chose the ASRock MOBO the price would be about $681
If you need to save money another way, you could possibly go for a cheaper SSD, though I think we are close enough on budget that I'd keep the PNY.
The PNY CS2211 is currently the cheapest 500GB MLC drive as far as I know, but the weaker TLC drives do cost less. They are slower and less durable, but good TLC drives are still faster than HDDs and should still last 5 years, possibly more. The OCZ Trion 150 I mentioned has gone from $90 to $110, but that's still a fair bit cheaper than the PNY currently. The OCZ has a 3 year warranty and the PNY has a 4 year warranty. Here's a comparison of the two drives (notice that sometimes lower scores are better, read the descriptions)
http://www.anandtech.com/bench/product/1650?vs=1675