Are there any fool-proof vegetables aside from the ones I've already
mentioned that a complete beginner might be successful with?


Well it depends on your definition of a fool, I suppose

Keep in mind I've never been to Ireland. Yet.
Cool season crops should do well now: lettuce, beets, peas, cabbage,
potatoes, beans. If you have good light (as in strong but not enough
to fry little plants) then you could start indoors tomatoes,
cucumbers, melons, squash.

Your little greenhouse might not be ideal b/c if too small, it's a bit
like your auto - fast to heat up. You need to keep it vented if you
don't want to crisp your seedlings!

Once you do have transplants to set out, you need to harden them off:
gradually get them used to life outdoors. A little sun, protect from
wind, etc.