Ok, a couple of points for you...
At the same budget point, I would expect a pair of floorstanders to beat 5.1 system for music use every time.
For film/TV, it would be up to the user's preference. 5.1 gets you the full surround effect, while the floorstanders would have better absolute quality. (2.1 is another option here too - fronts and a sub).
having just a pair of speakers means you can get a stereo amp instead of an AVR. For the same money this will get you a lot more quality, especially for music. (You will lose the video switching from the AVR, but this can often be done through your TV).
Yes you can definitely have floorstanders and a 5.1 hooked up at the same time.
Or... you can have a 5.1 system which has floorstanders as its front pair. In fact, one of the pairs of speakers you already identified comes as part of a 5.1 package:
Monitor Audio BRONZE BX5 5.1 Black | 5.1 Speaker System | Richer Sounds
Or if you prefer the idea of actually having two separate sets (5.1 and 2.0) at the same time, you can go down a switching route, or use the zone 2 output on the amp.
Also note that if you buy floorstanding fronts now, you can always buy more speakers to make it 5.1 in future, as budget allows. (Similarly, if you get a 5.1 set now, you can upgrade the front pair to something bigger. Then either discard the old pair or use them as 7.1)
To make your decision, I think you need to:
Decide what your budget is.
Decide if you want to upgrade in future.
Think about whether you value music or film/TV performance as a higher priority
Listen to some 5.1 and stereo setups, both for music and film.
Also, the amps you're looking at are all very new models. If you can still find last year's ones, you can get a level above in quality, for the same money or less.
Instead of the Onkyo 515/616, look for the 509/609/709.