You should've invested in CloudFront first because your site isn't loading.
Just curious, is there any general number range for how much traffic a front page post might get? Less than 10k, 10-100,000, 100,000+, etc
But as my blog is entirely static (except for the comment threads, hosted on my Discourse forum), I just let CloudFlare serve it. I had to do some tweaks to the configs to say, "No, really, cache everything!" (it doesn't do that by default for a range of very valid reasons, none of which apply to me), but once that change went in, I'll see 98.5% or higher "served out of cache" ratios when I'm seeing a lot of traffic from HN or somewhere.
I'd originally designed it to be hosted out of a Google Cloud bucket with CloudFlare (egress traffic is cheaper that way than out to the internet), but I eventually decided to host on my server, as I could then do Tor and some other stuff more easily. I've got the server anyway...
One of these days, I may play with dropping analytics entirely and just passing requests through to my server, let images remain cached as that's the bulk of my bandwidth. Then I can go even more oldskool and parse my server logs for stats and referrers and such!