Breadboard are for development and testing. When you are OK with your circuit, then you solder it.
Your alternatives:
Point-to-Point
Just solder directly component to component. You can arrange your component for minimal space and minimal wiring lenght. Can be very elegant (depends on your abilities); doesn't requiere any board.
Perforated board
For personal projects, you can use a perforated board to put all your components. Requieres some planning in components placement and wiring (you can paint yourself in a corner). Easy to do.
Expansion Shield
It's a perforated board in a shield, so you just plug it over your Arduino Uno. Great if you need easy access to lots of Arduino pins. Cons: little space for components. There are versions with a minibreadboard instead of a perforated board.
PCB
You can make your how PCB, but it's hard and too much work. Use it only for high volume production. It requiere lots of preparation and dangerous chemicals.
