What happens with excess items if my bag is full, and what should I do to avoid losing items?

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?

Solution 1:

If you are just under the limit(e.g. 349) and you activate a Pokestop you still get all the items from that stop.

If you're over the limit you won't get new items and only get 50xp. If you level up when you're over the limit you still get all the items from that level up.

Since you're still level 6 you don't need to worry much, although if you're running out of Pokeballs you can throw some potions/revives away.

Solution 2:

At Poké Stops: You will get a warning that your inventory is full and not receive any items when it's full.

At Level-Up: You will receive every item and it will show 380/350 to give an example.

The best strategy is to throw the revivers and heals aways in order that you always receive Pokeballs at Stops. Since you wrote that you don't participate in gyms anyway. Thus, Balls are most valuable for you.