You can not accurately estimate how much network traffic will be generated. There is nothing from stopping it from becoming immediately viral. Sites have had hundreds of thousands of visitors increases daily. Be prepared. Host the static on s3 etc... Engineer for it.
Varnish: https://www.varnish-cache.org/ A decent primer.
Failover database servers? Auto scaling on amazon?
A Fortune 500 is a big deal. Don't worry. This is a good kind problem to be having. Regardless, the exposure will continue and be referenceable which is great for your site.
You can guess, maxmcd gave some suggestions, but you can't really estimate. My web site has been shown on two national TV shows and I can tell you from experience that so many variables come into play that you can't even estimate the order of magnitude of traffic. With the cost of web servers as they are now, just prepare for the biggest amount of traffic you can imagine, overkill is better than under.
Does facebook have activity monitors of any sort? Can you ask them how many people visit the page directly or view their news feed items?
Let us know how it goes! What's the website?
There's a few ways I've gone about doing this in the past:
- Find out if they've ever done something similar in the past and see if you can get performance numbers on that post.
- Ask around and see if you can get some good Facebook click data numbers for the type of post you expect to get. These vary greatly depending on the brand but you can usually use engagement (comments and likes on individual posts) to see if different user groups are going to perform similarly.
- Do some basic back of the envelope math. Look at how many likes they have, likes per post. What percentage are going to click on your link?
Your best bet is usually the first one. Similar campaigns on the same page are going to offer you the best insight. Although, I've found that social media tends to fail to meet my expectations time and time again in situations like this. Depending on the company, you might not push that far past 1k/day.
Either way, good luck.