There are many different rules across airlines regarding luggage weight and size, with more and more short haul airlines only offering 1 free piece of luggage that fits under the seat. You then have the option of adding a cabin bag or larger suitcase for a fee.
If you are travelling for a weekend or just a few days you might be able to fit everything into the bag that goes under the seat. The space is surprisingly large (Ryanair 40x20x25) Easyjet has a slightly large option (45x36x20) and many backpacks or quite large bags will fit there. Some are very lightweight but sturdy and have many compartments to fit many items into. They also come in a number of different colours.
Here are a few examples of bags and backpacks that fit under the seat of an aircraft.
Under seat cabin bag Ryanair
Under seat cabin bag Easyjet
