This ended up being a very easy project to complete; Ana's instructions were very straightforward. I probably spent four hours altogether on the project, although that was spread over the course of several days.
We had several 2x4s left over from other projects, and I was able to use a quart of exterior Behr Premium Plus Ultra (with primer included) that didn't get used for its intended project. So altogether, we spent about $20. You can't even buy a plastic kids' picnic table for that price!
As for advice, I found that the best way to avoid wobbling was to firmly attach three of the legs while leaving the fourth leg somewhat lose. Upon flipping the table, you should be able to move that fourth leg into a place that prevents wobbles before firmly screwing it in as well.
I painted all the boards before assembling the table, and I feel like that is the best approach, as the space in between boards is slim.