Why was it that Yizhak originally chose to bless Eisav and not Yackov? I would have thought he would bless both of his sons equally. Why did he choose to only give the blessing to one of them?
Yitzchak did have equal blessings for both of his sons. He intended to bless Eisav with general wealth and prosperity. As it says in Genesis 27:28-29, "May God give you of the dew of heaven, and of the fat places of the earth, and plenty of corn and wine..." This is a blessing that Eisav should be well-off and successful in life. However, there was also a second blessing that was specific to this family - the covenant that God made with Abraham, that his family should inherit that Land of Canaan and that his children will be like the stars in the sky (Genesis 15). This was the blessing that Yitzchak intended to give to Yaakov - and he does give it to him, in Genesis 28:3-5. "And may God bless you and make you a mighty nation, and give you the blessing of Abraham, that you shall inherit the Land that God promised to Abraham." [Translation is mine.]
So you see that there are two blessings. Eisav was supposed to get a general blessing of wealth and success, and Yaakov was supposed to get the specific Abraham's Family blessing. However, Yaakov, at Rivka's insistence, jumped the gun, and took both blessings. Perhaps if he hadn't done so, the verses which tell us that Eisav hated Yaakov would have instead told us that Yitzchak invited Yaakov over so that he could bless him as well.
Don't just take my word for it:
- Rabbi Menachem Leibtag deals with this issue at length. You can view his shiur online at PARSHAT TOLDOT - ' the chosen son'
- Rabbi Yaakov Meidan proposes that Yitzchak intended to split the Abrahamic blessing between both his sons. (He still fully intended to bless both of them.) You can read his shiur here: Esav's Merit
Why did Rivka persuasade Yaakov to get both blessings? One answer is the one quoted by @Rony above. Or, perhaps Rivka simply misunderstood Yitzchak's intentions, and thought that he intended to give the Abraham-specific blessing to Eisav. Rabbi Elchanan Samet deals with this question, and you can view his answers here: The Moral Dimension of the Story of Yitzchak's Blessings (Bereishit 26:34-28:9)
There is an opinion which I heard in a shiur given by Rabbi Baruch Rosenblum, that Yizhak knew that Am Yisrael will be Malechet Cohanim (a nation of Cohanim) totally invloved in Torah and avodat Hashem, but for that you need a Zebulun that will take care after all the material needs of the Cohanim. He thought that Eisav would be this Zebulun and that is why he wanted to give him the blessing that dealt with what is needed to achieve this. Rivka knew that this had no chance and so the story developed the way it did. Yizhak had in mind to bless Ya'akov with the spiritual blessing, which he eventually did.
The answer here, from R. Schneur Zalman of Liadi, also addresses this issue. In brief, Yitzchak planned to bless Eisav because he thought that this would be the right way to redeem the spiritual "sparks" that he possessed.
Perhaps Rashi (Bereshit 28:15) is addressing the second half of your question when he says:
...What I promised to Abraham concerning his seed, I promised in reference to you and not in reference to Esau, for I did not say to him, “for Isaac will be called your seed,” [which would signify that all of Isaac’s descendants would be regarded as Abraham’s] but “for in Isaac,” [meaning part of Isaac’s descendants] but not all [the descendants] of Isaac (Nedarim 31a).