The retriever breeds seem to be among the worst for allergies, because whatever it is in their skin and coat that makes them good at dealing with water seems to make them extra stinky and allergenic.
We have a Chow mix that my DH is not allergic to. Her coat is so dense that nothing gets from her skin to the surface (or vice versa).
I thought our vacuum had a HEPA filter on it, and that the bags were HEPA rated, but recently I bought super fancy cloth-like vacuum bags that said they were for allergies, muttering at the expense. They cost 10x as much but the improvement in the air quality afterwards was apparent even to me, the non-allergic person.
If you have central air conditioning or heat, you can add a HEPA filtration system to it. We don’t have one, but I’ve heard they are well worth the cost. Even running it on a fan setting will clean the air.
Another thing that we do, that is not necessarily directly related to dogs, is that we take our shoes off when we come in. It does help somewhat with keeping the house cleaner. You might also try having a button shirt or light jacket that is worn when handling or petting the dog, then take it off and wash your hands when you’re done.
