Will trailer be my best option? If not, what is?
From your other question - your budget for the bike was 300 euros.  You'd spend that much on a trailer alone.

Trailers more than double your rolling resistance, and increase your windage area a lot.  Riding long distance with a 2 wheel trailer is unpleasant.

You might build your own trailer, there are many plans around the web for this, using a square of metal or timber, two wheels and either a seatpost or a rear-axle hitch.

Another possibility is a single wheel trailer, which carry a bit less but are more useable on singletracks and narrower roads.

Making a trailer with a locking bin could solve your security problem, but it still needs locking closed and locking up to something when unattended.

In order of preference, top of the list would be front and rear panniers, then a frame bag, then a trailer, then a rear rack with your pack on it, and lowest on the list is a backpack on your back.