No prior experience - looking for a general recommendation

hey friends, looking for some general advice.

• There is a ton of info online, so just wanted to hear from some of the community. Located in Australia. Apartment with two bedrooms + a mixed living/dining
• Sizes
  • Mixed Living/Dining - ~5m x 6m x 3m (90 cubic m)
  • Bedroom 1 - ~3m x 4m x 3m (36 cubic m)
• Minor pollen allergies, have a gas stove top, no mould, no smoking, no odours, no pets.
• Budget: Open, but realistically don't want to spend more than $300-500 AUD for the first year and $100 ongoing.

Partner has mild hayfever, but just wondering based on the above information if it sounds like an air purifier would be helpful/useful and worth the money (given there is an ongoing cost).

If we only got one for the living room or only one for the bedroom, what does that actually mean in practice? Does that reduce effectiveness? Mean that we need to keep doors closed?