On digital ocean you get a very limited set of boot options. You can't provide them your own installer, boot image, kernel, iso, or any of that jazz.
You also don't get a pre-boot console.
For linux, they don't even let you provide your own kernel in userland or the like, so there's actually no way to install a BSD from a linux shim on DO.
FreeBSD on DO is the only way to get an instance that is capable of booting anything non-linux, so it's necessary to start from freebsd.
This also probably works on other cloud providers if they support a virtualization layer that OpenBSD will work with. I've heard of successes here too: https://vultr.com/
Just be sure you use miniroot58.fs -- OpenBSD 5.8 wasn't released when this was written.
Vultr allows installing from ISO, so no need to shim. I can verify that OpenBSD 5.7-stable will run with no issues. One thing to watch out for is that outgoing TCP connections to port 25 are blocked until you ask them to open it up.
One can receive updates to binary packages for the current -stable release from M:Tier[0] . They also host binpatches for security vulnerabilities in base which can either be installed manually via pkg_add or automatically with their openup[1] tool.
Running -stable is fairly simple. If you don't want to rebuild on your DigitalOcean VPS, cut a new release after an update locally, and then apply it on your VPS. See http://www.openbsd.org/faq/faq5.html#Release. This should be fairly simple to automate (and you could even write a script that only packages up changed files if you were so inclined).
If you cannot run stable, then I'm pretty sure you should let others do your system administration for you. Stable is very easy to follow with simple instructions: http://www.openbsd.org/stable.html
Stable will cleanly build though, where running current snapshots you could come across something temporarily broken or have to debug a tough build if doing it from source. FWIW I just built 5.7 stable and the whole process took an hour and a half for kernel + userland + xenocara with no build issues. Often for stable security patches you just have to rebuild the kernel which is 15 mins work on my older AMD server.
I got it installed, but there were problems.
A lot of programs fail with SIGILL, illegal instruction.
OpenSSL fails in OPENSSL_ia32_cpuid()
Anybody get past this ?
I also get coredumps from openssl, ssh-keygen, and smtpctl on the first boot. The common factor for all of these is the XGETBV instruction - unfortunately it looks like DigitalOcean's setup of KVM doesn't support it.
This was just on amd64 though - installing OpenBSD for i386 seems to work okay, apart from sometimes hanging on boot (not sure why this is).
I have done a few bits with PXE booting inc OpenBSD, so I might be able to help if you can provide more detail. (I do feel your pain as PXE error messages are largely pretty vague, but not posting the error message is even less helpful).