The first part is choosing the LEDs: use a reputable source so you can get the datasheets to find out the spectra. Choose as many and as varied as you like -- these are all quite narrow beams (15 degree), quite bright, and go from ultraviolet to infrared. The graph shows the spectra from the datasheets, except the 400 nm LED which is an estimation.
Make it any way you like: on breadboard, on a circuit board, just-soldered-together. This instructable shows the housing I made with a CNC mill, which gives a nice turnable control, and keeps the light output in one place for easily fixing fibre optics. You could easily make one with laser cut materials, 3-D print one, or just solder it together on a piece of breadboard.