Ian, what phranque says, and also see this discussion from several months back... Will ccTLD "domain hack" hurt rankings in other countries? .ne for USA May 18, 2017 https://www.webmasterworld.com/google/4849981.htm
You clearly understand the basics, and are right in your hesitation about using .co ...which is a ccTLD that was intended for Colombia, but for now
, at least, is being treated as a gTLD by Google, because of relatively low demand in Columbia and because of somewhat common use as a generic substitute for "company".
Note, as Matt Cutts points out in the referenced video, the posted list is subject to change. IMO, problems you might run into are...
a) the list might change depending on future demand for local .co domains in Colombia.
b) the registration cost might grow larger over the years. I haven't looked into .co in particular, but I have seen some prices on these specialty names get fairly high.
c) my observation in (b) might also apply to the newer gTLDs, about which you're rightly cautious.
Take a look also at this slightly more recent thread, where I expand slightly on some points Matt Cutts makes... and I also note that several well-known brands using .ly TLDs have switched to "equivalent" .com domains which include the "ly" before the .com extension. Draw your own conclusions. Can a .DO domain be bad for SEO? June 16, 2017 https://www.webmasterworld.com/google/4853787.htm