For starters, I'd invest in tile or hardwood floors...
We have a local entrepreneur who fixes up & resells vacuum cleaners. We bought an upright bagless Dirt Devil with a 12-amp motor for $50. It runs, it cleans, we empty out the canister each time and vacuum the filter once in a while. All the parts seem tough, and nothing has snapped off or jammed. It works great. We've beaten it hard for over a year and it just keeps on sucking.
My mother-in-law has used a Hoover canister vacuum since her 1958 marriage (it was a wedding gift). Maybe it never breaks or parts are still available, but either way I hope I'm in that good a shape when I'm that age. We used to own a 2002-model Hoover upright (with a bag) but little plastic attachments kept breaking. When the wheel carriage snapped I finally quit trying to fix it and gave it to the vacuum entrepreneur.
I'd buy any used vacuum that has a high-quality air filter, especially a HEPA filter. If a HEPA filter is good enough to vacuum out the reactor compartment on a nuclear submarine then I think it can handle allergens and "infectious diseases".
I would never invest $300 in a vacuum cleaner. You could probably throw away a $45 Bissell every two years and still be ahead.
As for used futon mattresses, we buy the ones with washable covers. We've also furnished our whole house from Craigslist, including several beds. It's pretty easy to check the condition of a mattress. While I'm sure bad things can happen with used furniture, I suspect that the probabilities are very low and avoided through the application of common sense.