A 300w ATX size PSU should be more than enough for the GPU. Corsair PSUs are generally pretty good.
The one thing to keep in mind is that the mini PCIe interface only supports 1 PCIe lane compared to a PCIe in a desktop motherboard that can support up to 16 lanes. That means the mini PCIe is a huge bottleneck.
As an example, I believe a GTX 960 can use up to 8 lanes so if that is a GPU you are thinking about purchasing then it's performance would likely be severely limited by the mini PCIe's single lane. You'll get better performance than integrated graphics, but you will definitely not be able to tap the full performance of the GTX 960.