The Ashkenazik practice is to begin the recitation of Selichos on a Motzaei Shabbos, minimally four days before Rosh Hashanah. A popular source (Mishna Berurah 581:6 citing Eliyahu Rabba) for this is the fact that in conjunction with every yom tov the Torah introduces the korban mussaf in Parshas Pinchas using the word "v'hikravtem - and you shall offer" the particular additional sacrifice. In contrast, regarding Rosh Hashanah the Torah mandates (Bamidbar 29:2) "va'aseesem - and you shall make an offering", understood by the rabbis to infer that man should make himself worthy of an offering. As an animal in the Beis Hamikdash required a "bikur mumm - physical inspection" over a period of 4 days assuring and insuring that the animal is blemish free and fit to be offered, so too is man to introspect and examine his ways, thoughts, and actions that they are worthy and appropriate for the service of Hashem.
At first glance the particular krias HaTorah that is read on the Shabbos before Selichos need not be related to Selichos. At the same time, this year Parshas Ki Tavo is read and I believe that a careful understanding of the opening mitzvah of bikurim can shed light and enhance our appreciation of Selichos.
There are two mitzvos out of the 613 that deal with bikurim. In Mishpatim (23:19) the Torah legislates the mitzvah of bringing the first fruits to the Beis Hamikdash, and in Ki Tavo (26:5-10) the Torah provides an exact text of a declaration, mikreh bikurim, that the farmer is to recite upon presenting his first fruits to the Kohen in the Beis Hamikdash. The essence of this declaration is thanksgiving to Hashem for the produce, for the land of Israel, and for His directing history and redeeming the enslaved Jewish nation from Egypt and bringing them to the promised-land. Upon completion of the declaration, the farmer prostrates himself before Hashem.
Dovid Hamelech (Tehillim 50:23) says, "Zoveiach todah yechabdoneni" which can be understood in one of two ways. One way is: the one who offers a thanksgiving offering honors Me. The Talmud (Brachos 54b) teaches that individuals that underwent challenging and dangerous situations are obligated to bring a thanksgiving offering, including seafarers, those who go through wildernesses, one who was ill and recovered, and one who was incarcerated in prison and came out. Their offering, the prescribed korban todah, is a recognition of Hashem's divine providence, and thereby honors Hashem. Today, when we do not yet have the third Beis Hamikdash, we recite the Birkat Hagomel instead.
Rashi, however, understands the word "todah" not as thanksgiving but as an admission and confession. Thus the verse is to be understood as: the one who brings an offering of repentance and confesses his sins is truly honoring Me. It is interesting to note that the root of the word "todah" means both to admit and to offer thanks. Indeed, Rav Hutner zt"l noted that the two understandings complement each other in the beracha of modim, which is the theme of the final section of every Shemoneh Esrei. The Jew acknowledges and admits (as in modeh b'miktzas, when one admits to part of a financial claim against him). Here too the worshipper admits that he could not do it alone, that he needed the assistance of other. Indeed, every time we say thank you we are first stating that we needed something, and that we could not do it all on our own. Subsequently having admitted this reality, the second meaning of "todah" - thanks - emerges, and one expresses appreciation for the good they have received.
The Torah mandates that upon completion of the recitation of mikreh bikurim the farmer prostrates himself before the mizbeach - the altar of Hashem. The act of hachna'ah, of total submission to Hashem, follows naturally the detailed declaration of hakaras hatov - thanksgiving. The more one realizes that they have been the beneficiary of His bounty the more grateful and humbled they become and desire to reciprocate in kind, fulfilling His every wish.
The Talmidei Hagra share, in the name of their teacher, a related insight into the Shema. The opening line of Shema expresses the sovereignty of Hashem, Shema continues to tell us to love God with ALL our hearts, ALL our souls, and ALL our might. Why the threefold repetition of "b'chol - with all"? It is teaching us not only the existence and uniqueness of Hashem, but that ALL emanates from Him. Thus our hakaras hatov - gratitude is directed to one Source only, hence the three "all"s concretizing this idea.
There is an interesting difference of opinion when the ideal time is to recite the opening Selichos. Rav Elyashiv zt"l opined that it is best to say Selichos early Sunday morning. This is based on the words of the Shulchan Aruch (Orach Chaim 581:1) that the practice is to rise early to recite Selichos. The very rousing of one's self from their sleep and slumber sets the tone for acknowledging their sins. The motivation is one of todah - viduy - admission of guilt, i.e. not having actualized one's full potential.
The Leket Yosher (a student of the Trumas Hadeshen) taught that we recite Selichos on Saturday night going from the joy of Shabbos to the joy of Selichos. The joy of Shabbos emanates from the spiritual effect of greater and more meaningful studying of Torah on Shabbos, and the physical oneg - delight of Shabbos. The positive mood and delight of Shabbos is the ideal prerequisite for Selichos. This is the todah of thanksgiving leading to the todah of admission, namely in view of the excessive bounty that Hashem gives each and every one of us - B'ezras Hashem our health, our family, our environment, our sustenance - one realizes that we can never sufficiently repay Him and therefore we come to Selichos with a happy countenance, wanting to improve ourselves to give Him nachas.
The Medrash Rabbah explains the opening words of the Torah, "Bereishis barah Elokim", to mean, "for reishis - the first Hashem created" the world, and that "reishis" refers to the Torah, Bnai Yisroel (see Rashi on the opening verse of Torah), and Bikurim (which are called "reishis" in Shemos 23:19.) Now we understand why the world was created for Bikurim - its declaration of hakaras hatov sets the tone and foundation for man to serve Hashem. The attitude that it's all me is transformed to appreciate and recognize that everything comes from Him.
Thus, the Medrash Rabbah (Bereishis 22) teaches when Adam asked Cain what occurred after his horrific act of fratricide and he said "I did teshuva and was pardoned", Adam responded with "Tov l'hodos l'Hashem - it is good to thank the Lord". The Chasam Sofer cites the Medrash which explains, "Tov l'hodos l'Hashem" to mean "it is good to confess and accept total submission to Hashem". His beneficence leads to our character development. May we be ever aware and makir tov of His constant showering us with goodness and be thereby prompted to reciprocate and be worthy thereof.