1600 will more or less get you whatever you need. With Ryzen currently being as strong as it is, Ryzen is honestly a better option than Intel unless you're literally strictly gaming, and that's it.
Intel:
https://pcpartpicker.com/list/HGrZbj
Basically the case is personal preference, also not including Windows. You could cut back and get a cheaper M.2 SSD or a SATA SSD, but I have the 960 EVO and love it.
AMD:
https://pcpartpicker.com/list/TtPPpb
Only issue with this build is it's not an 1800x, but beggars can't be choosers. Also I'm not 100% certain the H100i v2 ships with an AM4 bracket.
NOTE: If you don't plan to overclock, you will not need water cooling, which saves you roughly $60-80 depending on what air cooler you buy (preferably Hyper 212 Evo)
Both are equally good, Ryzen is better for multi-tasking/streaming/editing, Intel is better for straight up gaming. If it were up to me I would go Ryzen, since the performance hit in gaming is minimal compared to the increase in multi-tasking and general workstation purposes.