It's been a bit over a week now on Azure, and so far it costs around 2kr per day - which is a bit over budget. After all - a fixed price of $5/month at SmarterAsp.net is about half that.
But I got a message from Cloudflare, that only 6% of my traffic was cached, so I started looking into that bit. as it turns out, a blog is fairly static - well mine is at any rate, so I'm thinking that if I add 24h TTL then I should be pretty much secured - except of course from attempts to hack the admin-part - but it seems Cloudflare attempts to help me there too by employing an application firewall - again free of charge.
I'll check back in a week to let you (and me) know how added caching affects my bill.