Beginning with "Bismillah , walHamdulillah , wasSalaatu wasSalaamu alaa Rasoolillah"
It is narrated that the Prophet (peace be upon him) said:
“A statement that does not begin with praise of Allah and blessing upon me, remains deficient and bereft of blessings.” (Abu Dawud, 13/184)
The same has been narrated about Bismillah also.
The Arabic letter Baa in Bismillah stands for seeking help. From a syntactical point of view it relates to a noun or verb dropped by aphasia. The Quran contains examples of its relationship with both verb and noun. The example of verb is Iqra bism-e-rabbika (Read: “In the Name of your Lord…”) and the example of noun is Bismillah-e-majreha (In the Name of Allah will be its moving course).
Hamd means praising orally a grace regardless of being benefited by it, be it a favour or anything else, such as a statement that ‘I did Hamd of a certain person in connection with the prize he had been awarded or for his feat of boldness.’ Shukr (thanking) is that praise which is done orally or emotionally or by any other organ of the body in lieu of some favour. This shows that the word Hamd is commonly used in one situation and the Shukr in another situation.
Describing the mutual difference between Hamd and Madh (praise) Ibn Al-Qaiyim writes that Hamd denotes stating qualities with love and respect; and Madh denotes only declaration of the quality, it does not necessarily imply love and respect. That is why the connotation of Hamd is of a special nature and that of Madh a general.
In the word Al-Hamdu, the prefix Al has been used comprehensiveness meaning that it includes all forms of Hamd. Some people have described it as a generic noun and have maintained that perfect Hamd is affirmed only for Allah. This word shows that Allah has all the Attributes of perfection and beauty.
Source: Sharh Al-Aqeedat-il-Wasitiyah – by Shaikh al-Islam Ibn Taymiyyah