Basement – the intended plan with this basement rough-in plumbing

Yes, you are in an excellent position to add a basement bathroom.

Definitely involve a competent plumber in this process. Properly venting and properly attaching the new waste drains to the existing waste drain will be important to prevent the basement bathroom traps from being sucked dry when waste is leaving the upper floors. This is an easy part to mess up in a renovation like you're suggesting.

Ideally, you would have used rigid insulation against the concrete. This would have worked as both your insulation and a vapor retarder (but not barrier). These days, vapor barriers are frowned upon in basements, as they ultimately lead to trapped moisture somewhere.

The only exception is closed-cell spray foam. That acts as a vapor barrier and insulation, but since it's applied directly against the concrete sans air gap, there is no place for water to be trapped in the first place.

Given the budget, I'd strongly recommend the spray foam solution.

Barring that, skip the vapor barrier, make sure the bath is properly vented (fan), and use a 'tile-side' waterproofer for your tub surround such as Redgard.