Which opening sentence most strongly engages the reader and provides context?
the weekend was dreadful with bad weather, foul bugs, a bigfoot sighting, and the worst camping trip in the 5 of camping trips.
we could have had a worse weekend, but it's awfully hard to beat bigfoot and bugs.
we could have picked worse weather for fighting off mosquitoes, bigfoot, and an army of ants, but even without torrential downpours it was pretty much the worst camping trip ever.
when your weekend goes from bad to worse, it might not do to go camping with ants, mosquitoes, rain and bigfoot.

Of the opening sentences that were presented here that strongly engages the reader and provides context to them would be the second one which is "We could have had a worse weekend, but it's awfully hard to beat Bigfoot and bugs."

The first and third one were just not good enough because it exposes the rest of the context to the reader and lets them have the idea of what you are talking about which usually leads to the readers not choosing to continue to read, thus taking out the reader's engagement but still provides context. The last one is better than the first and third, but it spilled the beans when it mentioned the particulars as to what made the weekend bad to worse. The answer is just right. It has the impact that would hook the reader to know more about your weekend and why is Bigfoot and bugs together in your statement. The rain wasn't mentioned which would be ideal to make the story telling take a turn to much worse which would spike up the interest of the reader.