Personally, I would not use InDesign for a one-page poster. There are a few advantages to InDesign, but for things like these I greatly prefer the free-form nature of Illustrator. Others, who prefer using InDesign for various personal preference reasons, will feel otherwise.
As for using only Photoshop, it becomes more problematic. The rule of thumb is to avoid using Photoshop for type — especially text. However, in reality it sort of depends on whether or not one knows what he or she is doing.
Using traditional printing terminology (digital complicates things), when colored type (or any shape with hard edges) is composed of screen tints, the resolution of the edges can be no greater than the screen frequency of the halftone dots making up the tints. When this is the case, it really makes no difference to quality whether or not the typography is rasterized to a 300 ppi image or not since the printed output will be the same — likely 150 lpi screen tints.
When using solid black or spot color type, however, it makes sense to stick with vector imagery since the output will be rasterized by the RIP to the resolution of the platesetter (likely several thousand dots per inch), which creates very smooth edges on small type. Rasterize this type in Photoshop — even as 100% K in CMYK mode — and you’ll reduce the resolution of those images to the more course resolution of the image bitmap which is likely around 300ppi.
Of course this doesn’t address the other benefits of using vector objects, like the ability to move them around easier and adjust their shapes.
However, out of the three posters, I’d say only the second one would benefit quality-wise from using Illustrator, and that’s for the simple reason that it has a number of solid black shapes and black typography that would be best printed out at full platesetter resolution rather than the resolution of the raster imagery behind it.