The mini pump should come with a bike mount which will fix to the bike using the water bottle fittings underneath the water bottle holder, that's how I carry mine, I think they are too big to fit inside a seat post bag. I use Topeak seat post bags with a quick release clamp to carry my spare inner tube, tools in etc and just change the size of the bag I have to suit the ride I am going to do. Without going to look, the Topeak bags have elastic underneath to carry a pump, but I feel that they are not too secure.
But as for seat post bags, these have caught my eye which someone posted a link too the other day on the forum and that is probably what I will buy in the future, as the price is better and also there quick release without having to fit clamps to the saddle.
Alternatively you can carry the pump, innertube and tools in the back pocket of a cycling shirt for shorter rides like a lot of riders do.