Pro Mini

Roborock vacuum running on a schedule and a Medify (hospital-grade) purifier.

I can second this suggestion- it's a great model!! I'm not confident the air is going to mix down a very long hall to the kitchen by itself (regardless of the cadr of the purifier). If you had the stovetop exhaust fan on pulling air through, or just a regular fan somewhere on low, that might get air moving in from the hall, into the kitchen, so the purifier could pull it through.  Re: bathroom- it's my understanding humidity isn't good for HEPA filters and that there's a usage range, but I've operated small ones on bathroom countertops okay. I don't live in a humid area, and my bathroom does not get super steamy. I used the smaller levoit, and a small medify model. (Sorry don't recall model #s).

I have two dogs in a townhome and have 3 air purifiers. Absolutely love them. No dog smell. I have one Medify and two Levoit. Just make sure you get one that can actually clean the size of the space it will be in. The downside is buying the filters, but I find it worth the cost, and you can find cheaper, off-brand filters on Amazon.

medify needs more love. those medical grade H13 filters are legit

I've been using Medify Air for 5+ years and they've held up well. They work well, especially during wildfire season. I also run them when guests are present to reduce the spread of airborne germs for an immune compromised household member.

We use medify air purifiers

Medify, Coway, Honeywell are all brands I use and trust. And I’ve tried MOST brands. One I DONT recommend is Sans. They’re overpriced pieces of junk.  Just pick one based on sq footage and where you want the airflow (example if you want it to blow out the side, you may feel more of the breeze, or from the top) 

There are some HEPA air purifiers that are H14 rated. I use the Medify one and it works great.

Honeywell, Levoit, Medify, Coway

It depends on the size of your rooms, and how much noise matters to you. They will all be great for pet hair, dust, and have models at about $250 to $300, for your total $600 budget for 2 units -- but you need to get models that appropriately cover the square footage in each room. Typically models will advertise the square footage they cover on the highest setting -- which is the loudest. You want to be able to run it on lower settings most of the time, so check the square footage they cover on lower settings, and/or "overbuy" for your space. Also check the pricing for a unit's replacement filters -- that's an important cost consideration. Finally, if you can swing it, I also recommend units with activated carbon / VOC filters for smells, when you have pets :)

tbh they're all basically the same. just get whatever's on sale at costco that has a hepa filter. i got some random medify one for $150 and it works fine. people overthink this stuff way too much lol