Vacuum Recommendations

Need some help. I’ve read and read this sub and have only confused myself more. I have a Dyson stick that I love for its ease of use for quick pick-ups but I need something to really clean. 3000 sq ft 3-story house. Bottom floor is a finished basement with cheap vinyl flooring and 3 rugs. Main floor all wood. Stairs and top floor carpeting. Also have 3 cats and 2 litter boxes. And 2 older kids. Can only budget up to $450. I’d like to be able to vacuum under the beds. What do you recommend? Thanks!