Most suitable flooring for RA

I live in Sydney, Australia and I am 60 yrars old and have RA in all my joints except hip (touch wood!) and have had a double knee replacement.I have been on Humira for a bit over a year and it has made a world of difference (again, touch wood). Because I am currently feeling okay, I thought I'd have some work done around my house. I want to get rid of the carpet because It's actually due to be replaced and I find carpet to be too high maintenance. Basically, I can't/don't want to vacuum much any more, plus I never clean up spills in a timely fashion.

I was wondering if people could give me recommendations for a flooring that is
1. non skid
2. provides a certain "bounciness" in case I fall - I haven't for years, but it would be just my luck to do so the week after I have something installed
3. easily maintained and forgiving of carelessness on my part.

I know carpet would be the best for falls, but I just don't want it any more. Where i live doesn't get very cold, so carpet isn't necessary for warmth. I am leaning towards vinyl planks which seem to be more expensive than I anticipated, so I don't want to make a costly mistake.

Can people please tell me what flooring they have found to be successful?

Thanks, Therese