I currently have 17.01.5 installed on an mvebu linksys-wrt1900acs.
Is it correct that I am going to go here to download the correct version of 18.06.1? https://downloads.openwrt.org/releases/18.06.1/targets/mvebu/cortexa9/
And is it okay to install 18.06.1 by doing a sysupgrade on 17.01.5?
In general, and your device may have specific requirements that I'm not aware of, sysupgrade will successfully upgrade a 17.01 release to an 18.06 release that uses the typical /rom/ and /overlay/ filesystem (use of extroot has complications with upgrade, in general). You will need to reinstall any packages that you have manually installed.
As with any upgrade, I'd suggest taking a backup with LuCI, sysupgrade -b, and/or tar and putting it somewhere safe, "just in case". Capturing the output of opkg list-installed will help you identify the packages you previously had installed. There have been some scripts posted to help with package re-install as well.
There is "no guarantee" that moving from one major release to another (or from one architecture to another) will not change the config you need to run. However, experience between 17.01 and 18.06 release versions has generally been smooth for most users on most devices.
I'm okay losing my config. I'll rebuild. I just want to make sure there's no danger of bricking or something damaging happening by using sysupgrade. I want to make sure I shouldn't use another option when moving between major releases.
I'd scan/read through https://forum.openwrt.org/search?q=upgrade%20wrt1900, as well as reading the page on the current wiki to make sure there isn't something "different" around the WRT1900ACS
Thanks. I had no issues with flashing the sysupgrade image.