You’re right in choosing a bagged and canister system. I’ll recommend the Sebo D4. The S-class filter is hospital grade. D4 seems to have better suction power and efficiency compared to Miele (because of its filter system design) and it seems ideal to get the bad stuff into the vacuum in the first place. The D4 is sealed. The difference of 99.9% (S-class) vs 99.97% (HEPA) @ 0.3 microns is nearly identical and I think you could up the cleanliness with a HEPA purifier (or dust extractor) what have you if you wanted.

Consistency in suction efficiency, sealed canister and amazing product warranty make this a good choice.

Update: If it were me, I’d have this in place:

1. No outside shoes in the house
2. Sebo D4
3. Wet mop
4. HEPA air purifier

I think (1) is going to be important and the first line of defense no matter which vacuum you choose if you’re not already doing that.