What does "Min ha'Ba b'Yado" mean?
Rashi #1 and Targum Yonasan: It means that he took from his possessions.
Rashi #2 and Targum Onkelos: He took precious stones and jewels, 1 which a person tends to wrap and hold in his hand.
Rashi #3: From the Chulin that remained in his hand, after he had taken Ma'aseros from his possessions. 2
Targum Onkelos: He took from what he had brought with him.
Targum Yonasan and Ramban: He took from what was available to him. 3
Ha'amek Davar: It implies things without their own Da'as; that excludes slaves. He did not give a gift from them, for one may not sell [an Eved Kena'ani] to a Nochri, for he uproots him from Mitzvos (Gitin 43b).
Hadar Zekenim says that it is jewels, and also birds (trained to seize things) that officers and soldiers keep on their arms.
He fulfilled the promise that he made to Hashem earlier (Bereishis 28:22).
He was only able to send Esav sheep and cattle, because, since he was traveling, he did not have the means to send him silver and golden vessels and trinkets (Ramban).
Why does it say that Yaakov lodged, and afterwards sent the gift?
Malbim: He thought that perhaps he will have a Nevu'ah that night. When he saw that Hashem's word did not come, he took a gift for Esav.
Ha'amek Davar: When he saw that Esav did not come that day, he nullified the division into two camps, and lodged calmly and sent a gift.
QUESTIONS ON RASHI
Rashi writes: "'[From] what had come in his hand' - ... According to the homiletic Midrash, [this means] precious stones and pearls, which a person wraps up and carries in hand. Alternatively, ... he separated Ma'aser, and [only] then gave the gift." How can these two interpretations be derived from our Pasuk?
Gur Aryeh: The verse could have said, 'he took from what was in his hand;' whereas "what had come into his hand" implies the Chulin that was left as his portion, after tithing. The verse also could have said, 'What had come to him;' "in his hand" implies precious stones that are carried by hand.
