There's a default limit of 350 items in the bag (even though you can expand it through the shop). I am currently level 6 and have already ~250 items in my bag. I haven't done any battles yet, as all the gyms in my area are too strong for my pokémon at the moment. So I have a lot of Pokéballs, Heals and Revives that I don't need right now.
What happens once my bag is full? Will additional items go into a temporary overflow bag? Will I just lose them? Will they replace older items?
I'm afraid I will lose the valuable items gained through a level-up. Should I throw away items to avoid that? If so, what should I throw out first? Heals and Revives, as I don't need them right now? Or will they become too valuable later on and I should rather throw out some Pokéballs as those are the most common items to receive from a Pokéstop?
TL;DR: What happens with items that exceed my bag size limit and what is the best strategy to avoid losing valuable items?