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

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.

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.

From my experience of levelling, once you hit the 350 item limit:

Items gained from trainer level up WILL go into your bag, exceeding the limit. I've had 395/350 by doing this.

Using a Pokestop will gain no items, with the message "Your bag is full". You will still gain 50 exp from using the stop though.

At level 6, this isn't too much of an issue, from level 10 onwards though you may want to drop unused lower tier potions and Pokeballs to free space for Greatballs/Masterballs and Super Potions though.