Settling a few more cities might be a bad idea since the land around your empire isnt that great so you might want to wage war with cyrus, scout his lands a bit first and get a nice army of horsearchers (tech archery and horsebackriding to get them), use them to crush cyrus.
I don't think he needs to do an early attack on Cyrus. While its hard to tell because his explorer didn't get very far before getting killed, he has a lot of land to expand to the west, and some of it doesn't look that bad, lots of floodplains.
Looking at the post-Stonehenge map (which shows your exact location in the world) it appears that Cyrus is backed away into a corner of a continent. It should be easy to choke him into a hopefully small empire. If you place your next city in some good spot directly south of your capital and block off the entire passage, leaving your borders closed. Unless he has a decent amount of room back there, this will leave him crippled for the rest of the game, to be destroyed at your convenience.
Though you might want to open borders for a build to scout out his lands or spread your religion... just make sure you close them if you see a settler scuttling past your borders.
At any rate, as of now you aren't in danger of being closed off, just keep expanding south and west. An early rush can be tricky to do and I wouldn't recommend it on a first game, before you've ever fought a proper war with seige.
Edit: And don't worry, you're doing fine. The three major mistakes I've noticed people make early on (including me!) are...
1. "Collect all the shineys", building every wonder they can left and right without selectively building the few that'll actually help you in your situation. In easy difficulties you can get away with this, giving you a rude awakening if you try to move up.
2. Woefully under-expand, expecially if trying to place peaceful. Just because you're going for space race doesn't mean you can get away with a four or five city empire. (unless you really know what you're doing) This typically results to strong starts due to little maitenance but falling way behind in tech and power at the end game.
3. Neglect your military until you get a rude awakening by a twenty unit stack on your borders. Whoops!
I have to admit that I fell for all three of these in my first game, which I purposely played without reading guides or threads here just to see how well I'd do on my own.

Lost my military in poorly fought wars, left me unprotected... in retrospect I find it kind of surprising that 20-man stack appeared at chieftan/warlord level... wasn't very nice. And after introducing my friends to the game and reading some "just moved to noble-- need help!" threads, these seem to be the most common factors.
Avoid these and you should be golden.
