When Avraham Avinu returns home victorious from his battle with the four kings after rescuing Lot from their hands, he is greeted by Malki-Tzedek, the king of Shaleim, who brings out bread and wine and subsequently blesses both Avraham and Hashem (בראשיח י"ד:י"ח-כ). Although at first glance this appears to be a very noble gesture, appropriate for one described by the Torah (שם פסוק י"ח) as a Kohein, the Gemara in Nedarim (דף ל"ב:) finds fault with his actions because of the order in which he pronounced his blessings. As the Pesukim indicate, Malki-Tzedek, identified in the Midrash cited by Rashi (שם) as Shem, the son of Noach, first blessed Avraham and then Hashem, thereby praising the servant before the Master, which is obviously out of order. The Gemara concludes that because of this, Hashem decided that Malki-Tzedek's descendants would not all be Kohanim as he was.
The Sdei Chemed (מערכח ברכוח סימן א`אוח מ"ה) presents an interesting discussion among the Poskim based on this idea which frequently has relevance when people get together at a Kiddush or a Simcha and wish each other a "L'Chaim" over a cup of wine or liquor. Is it appropriate for one to fist say L'Chaim to a friend, blessing him, and then to make a Beracha to Hashem and drink the wine or liquor, as seems to be common practice? Or is it preferable for one to first make a Beracha, then drink something immediately, (to avoid any interruption between the recitation of the Beracha and the consumption of the drink) and only then wish one's friend a L'Chaim so as not to repeat the error of Malki-Tzedek by blessing Hashem only after blessing a fellow human being?
The Sdei Chemed cites opinions on both sides of the issue. Some hold that since the Gemara says that Malki-Tzedek was ultimately punished for failing to acknowledge Hashem before acknowledging Avraham, then we certainly ought to be careful to recite the proper Beracha to Hashem before wishing L'Chaim to any friend. Others, however, point to the Gemara in Berachos (דף י"ט:) and other places which states that Kavod HaBrios, giving honor to or preserving the dignity of another person, can sometimes take precedence even over the concern for avoiding the violation of an Aveirah from the Torah. Certainly, then, it should not be a problem to honor a friend by wishing him a L'Chaim and then to make a Beracha and have one's drink.
The Kaf HaChaim (אורח חיים סימן קע"ה ס"ק נ"ה) quotes one Posek who writes that he asked his Rebbe why he was careful to always make the Beracha and drink something before wishing the others at the table well and was told that it is improper to honor a person before honoring Hashem, presumably a reference to the aforementioned Gemara in Nedarim. But he adds that he disagrees with his Rebbe for two reasons. First, he mentions the Gemara in Berachos which places such a high value on the honor to be given to human beings. Then, he quotes a statement from the Maharshal in his "Yam Shel Shlomo" on Bava Kamma (פרק ח` סימן ס"ד) concerning how one should respond after being wished good health upon sneezing. There is a long-standing practice to wish someone well (using one expression or another) upon hearing him sneeze; Rabbi Akiva Eiger, in his Gilion HaShas on Berachos (דף נ"ג.) says that the source of this custom is founded in Pirkei D'Rabbi Eliezer (פרק נ"ב) where it is explained that originally one died by sneezing, as his breath left his body. Now that this is no longer true, one's life and health should be toasted when he sneezes. The Maharshal writes that there is also a practice to recite a Posuk to thank Hashem, but that this Posuk is to be recited by the person only after he acknowledges and thanks those who wish him good health. This ruling is accepted by the Magen Avraham (או"ח סימן ר"ל ס"ק ו`); apparently, there is no problem blessing Hashem after blessing a fellow human being. Nevertheless, this Posek concludes that he tries to follow his Rebbe's practice of first saying a Beracha and drinking before praising any human being or wishing anyone well.
The Kaf HaChaim continues by citing Poskim who reject the comparison to responding after one says "G-D bless you" or the like following a sneeze because the Maharshal himself bases his opinion on the statement of the Gemara in Bava Kamma (דף צ"ב:) that when one prays for the well being of a friend and is himself in need of such a blessing, he himself is answered first. Therefore, specifically in such a case, it may be permissible to respond and bless one's friend before blessing Hashem. Moreover, there may be a difference between responding to someone who has wished one well and initiating a blessing on one's own before saying a Beracha. The Maharshal's case may, therefore, have no bearing on the question of saying L'Chaim before reciting a Beracha. The Kaf Hachaim thus rules that honoring Hashem should take precedence and that therefore one should not say L'Chaim until after making a Beracha and taking a drink.
Rav Tzvi Pesach Frank, in his "Mikraei Kodesh" on Yomim Noraim (סימן ז`) discusses when to recite the "Yehi Ratzon" over the apples and other special foods eaten on Rosh Hashanah night, in relationship to the Beracha required for these foods. Citing a Gemara in Berachos (דף ל"א.) which says that one should first praise Hashem before davening to Him, he rules that the Beracha (and a bite of the food) must precede the Yehi Ratzon. He then quotes an authority who says for the same reason that one must first make a Beracha and take a drink before saying L'Chaim to a friend. This seems to be the preferred view among the Poskim.