As pointed out, the actual question is what are the maximums. They are both 1,000.
The starting sizes are:
So at +50 per upgrade, the most you need to buy is:
- For the items: (1000-350)/50 = 13 upgrades
- For the Pokémon: (1000-250)/50 = 15 upgrades
To see the current size, you can view via:
Select the Pokéball menu button > Items
Select the Pokéball menu button > Pokémon
At the top it says e.g.
Note that you can go over the limit - I think it is only Pokéstops that prevent you gaining items right now but haven't checked for sure.
It might just be important events like levelling up that allow you to go over.