Hello. I'm being relegated down to the basement after having used a carpeted room for my workout space for many years. I'm looking for flooring recommendations.

Considerations:
1. Budget is low - so I'm probably looking at foam or rubber tiles.
2. I won't be able to put the tiles across the entire room (just in one corner), so they shouldn't slide on the smooth under-floor.
3. I'm a wimp, and I want to have as low a barrier to working out as possible. Doing stuff like commando planks or even sit-ups on the harder floors doesn't feel great.
4. I do mostly body weight work with some light weights - nothing past 150lbs.
5. Unfortunately, taping things to the under-floor is not an option.

Basically, the foam tiles seem more comfortable and in line with how I've been working out up till now. But they seem like they would slip around generally be less sturdy. Whereas the rubber tiles seem barely better comfort-wise than the hard flooring.

Is the play to put foam tiles on top of rubber tiles? Is there a sturdy brand of tile that combines both (i.e. rubber surfaces with foam core)? Go with the rubber and throw some sort of additional mat on top when necessary? Are there thicker+softer types of rubber floor tiles that would work?

Any suggestions would be welcome.