What should I use the coins to purchase?

I would but the 300 bullet pack if you have enough coins, but once these bullets are shot, they are gone - you can carry what you have left to the next game, but you'll need to buy more packs if you run them out - unless you are happy to start with the free 50.

You can also upgrade the power-ups so that they last longer.

Save up 50,000 coins to unlock other characters.