Here are a couple pages with a bunch of interesting typeface pairings.
But first, a couple comments.
Body copy on the web used to be presented predominantly in sans serif fonts because on 72dpi 1024 x 768 screens it was a lot easier to read. Nowadays with the advent of retina screens and 1900px monitors it's not such a problem to read serif type on screen. Here... this is Georgia and it looks pretty nice, eh? It's one of my all time favorites. Like the blues, I just never get tired of it.
These days, top designers are using serif fonts for body copy. Look at http://www.wired.com/2016/02/zika-conspiracy-theories/
and at https://stuffandnonsense.co.uk/process
Personally, I am not a fan. I like sans serif type for body copy. I also don't like the current flat design trends. But, I think in order to look modern and professional it's important to follow these trends.
So, here are a couple pages with a bunch of nice Google font combinations.
This first one is really nice. Each pairing gets it's own mini-design. Look for the one about the fox and the grapes, and notice your cursor. Click on the grapes?
The next one only has a few, and much more simply and directly presented.
I looked at a bunch of magazines in my reading pile and they seemed to be split between serif and sans for body copy. Some even had a mix of types in different articles.
Another thing to consider is that it's not just about headlines and body copy. There are also captions (where sans still makes a lot of sense) sidebars, callouts and other elements which might not strictly follow the rule of Header & Body. The choices you make for these other elements can add a lot of polish to your design.
There, those are my thoughts on types of type.