For something small (assuming it is), you can get away using Unicorn as your Rails server (assuming Rails), you can spawn a worker inside your dyno using before_fork and #spawn.

For SSL, you can use CloudFlare as your DNS and take advantage of their SSL feature.

While not ideal, does it need to be ideal for a trivial, probably-not-super-high-functioning-hacky-app?

There's always Cloud66 — which I've used to great success. I have two servers (e3/32GB/4x250gb enterprise SSDs in HW RAID on nice pipes for less than $100 a month) that I rent, threw vSphere on it, hired a $50/month competent and trusted off-shore sysadmin team, and loaded up a couple VMs.

It's not completely ideal, and I understand I'm trading stability for a couple bucks, but in scaling my clients have saved a bunch.