vocologists say:

Sequence your warm ups in the same order infants learn to make sounds in early developmental stages. 

This order of sound making follows from the automatic reflex and regulatory systems.

You can use many different combination of sounds for each step. The point is that each step adds a level of complexity to the previous step, or a "modulation" to the original "carrier signal". Visit the Build Your Own warm up page for more ideas.

---

19th century voice teachers say:

In Stephen F. Austin's article, "Building Strong Voices -  Twelve Different Ways", he looks at 18th and 19th century pedagogy and the  most commonly practiced order of exercises they used to build up voices. Through an investigation of tested practices from previous eras, it is possible to see what methods have changed, and which ones remain useful.

Manuel Garcia (1805-1906)

1. Sustenuto - Sustained tones
This was believed to build a strong core to the sound and the exercises began in the lower part of the voice.  The low part of the voice was believed to be a foundation for the entire instrument.

2. Portemento - Slides
This was to build smoothness and continuity in the voice. It was meant to encourage  "a controlled, fluid exchange of dominance between opposing muscles".

3. Legato - Connected tones
Legato exercises  were meant to build off of the portemento slides.  "Portemento provides the technical foundation for connecting tones without discrete motion or sliding". 

4. Onsets - starting the sound
There were many arguments, even in the 19th century, about how much pressure should be used with onset exercises. Manuel Garcia argued that pressure should be built up before the onset in order to get optimum closure in the vocal folds (coup de glotte or 'glottal attack'). Many other argued the onset should be balanced in order to avoid injury.

5. Building up the TA muscle (the heavy muscle) into the upper part of the range
The generic term 'chest voice' is used to talk about using a 'heavier' sound in the higher part of the range. Many exercises went up to the pitches C5 or E5.

6. Stability in laryngeal height
These exercises included singing vowels that encouraged rounded lips and a lower larynx posture throughout the entire range.

7. Fast moving exercises
Getting the voice to move quickly was believed to get the voice to move freely. "A flexible voice is a free voice".

8. Staccato - Separate tones
This was believed to build up the coordination of the laryngeal muscles in charge of opening and closing the vocal folds (the arytenoids). "Staccato is correctly produced at the larynx while breath flow remains constant. It is produced by opening and closing the glottis".

Disclaimer:  We have tried to give credit to all of the images that we've used that are not our own, or believe them to be in public domain. 
If you see something that is yours that you feel is being used without proper permission, please let us know and we will gladly credit you or remove it.  Thanks for your help!