Matrix board is the next step up from breadboard prototyping.
The connections are to be soldered to the board and therefore are more secure, and allow more current to be transferred. Also, you have more flexibility with the placing of components. Unlike a breadboard, the wires should be made by soldering a wire to the board.
Matrix board can be obtained in a lot of varieties, lines and dots are mostly used.
When using the lines type, lines that should not be connected can be cut with a knife.
Use one ground (-) line from the power supply and one power (+) line as the outer board lines. Doing so, you can build up your circuit like the schematic you drew up. Connect a capacitor between the power lines for increased stability and less susceptibility for external interference. You can also look at the soldering tips.