That's rather like asking "how many gallons of petrol would it take to drive from London to Edinburgh?" when you don't specify what sort of vehicle you are driving. We need more details.
All depends on the quality of your photos and therefore the size (in MB).
I thought that the average size would be 5 MB, so I just checked 3 random pictures in my phone:
5.49 MB, 6.92 MB, 5.80 MB
Even at an average of 5 MB per picture, you're gong to need 20 GB of storage, so I'd go for a 32 GB stick - all depends on the quality of the pictures though ...
There are two main variables that affect the files size: The sensor size and the compressibility of the content.
My Sony has a 23 Megapixel sensor, and a casual glance at my photos give file sizes between 3.4 and 6.9 MB, which would seem to imply that I'd need around 20GB to store 4000 photos.
Whatever size you decide to buy, buy two of them so that you have two copies. It's amazing how many people believe that digital media is foolproof and will last for ever. It isn't and may not. For the sake of a few pounds you could lose the whole lot.