What basic addition is the current Pasuk coming to make to the preceding Pesukim (15:1-3)?
Seforno: Until now, the Shirah was referring to destruction of Pharaoh and his horse exclusively; whereas now, it deals with the destruction of his army and elite officers (together with their chariots). 1
Maharal (Gevuros Hashem Ch. 47, p. 189): It makes no difference to Hashem whether His enemies are many or few, or whether they are strong or weak. Pharaoh had a vast army, and Hashem "threw them down into the sea;" and the best of his officers were mighty warriors, yet "they sunk in the Yam Suf."
The structure of the Shirah is then as follows - Pasuk 1 states the first aspect of the miracle (the downfall of Pharaoh), then the following two Pesukim (2-3) praise Hashem for it. Pesukim 4-5 tell the second stage of the miracle (the destruction of the Egyptian army and officers), and Pasuk 6 offers the praises for it.
Why does the Torah refer to officers as 'Shalishim'?
Because the number three (Sheloshah) denotes strength. 1
I once read that the triangle is the most popular shape used in building bridges, because it is virtually impossible to knock it out of shape. It is also noteworthy that Yisrael descends from three Avos.
What are the connotations of "Tube'u b'Yam Suf"?
QUESTIONS ON RASHI
Rashi writes: "Mivchar" - This is a Shem Davar (a noun)." What does Rashi mean?
Gur Aryeh: Rashi cannot mean that "Mivchar" is a Shem Etzem (true noun) as opposed to a Shem To'ar (verb-based noun). 1 Rather, Rashi tells us not to mistake the 'Mem' as an indicator of a present tense verb (e.g. in Hif'il or Pi'el). "Mivchar" is not an actual verb, but rather, a noun.
Gur Aryeh: a. The examples Rashi gives are, in fact, of Shem To'ar - "Mishkav, Merkav" (Vayikra 15:4, 9); "Mikra Kodesh" (Shemos 12:16 - and see Gur Aryeh there). b. "Mivchar" as a true noun would mean 'the choosing of [his officers]'; and 'a choosing' is not a tangible item that can be 'sunk in the Yam Suf.'