1) While davening Shemona Esrei it is important to stand straight, without leaning on a table, shtender, or anything else for support.
Even if one is leaning lightly enough, that if the object he/she is leaning on is removed, they would not fall, it is still forbidden.
The reason for this is that by Shemona Esrei one must stand in awe, as he/she is standing before the king [of kings], and leaning on something, no matter how lightly, is a lack of awe.
Simply placing the hands on a table or shtender is permitted.
2) If one davened while leaning, it is no worse than sitting, and the Shemona Esrei need not be repeated (Pri Megadim based on the Rambam)
For other things that one is Halachically required to stand (e.g. Chazaras HaShatz, Tekias Shofar, Halel, when a Sefer Torah is passing by, Vidui etc.) it is permitted to lean on something if done lightly enough that if the item was removed you would not fall, as the reason there is for Kavod and not because of awe, as it is by Shemona Esrei.
Reader's Question:
[You wrote that] The Vilna Gaon, Chazon Ish, The steipler, Rav Moshe [Feinstein].... all did not kiss the tziztis during shema, is this the halachically better way to only kiss them after Emes once shema has been completed?
My Answer:
True, many Gedolim who followed the Gr"a did not kiss their Tzitzis during Shema. Yet, many Gedolim did - and still do- kiss their Tzitzis during Shema. Both opinions have strong basis in Halacha.
It is not for me, nor for anyone alive today to determine which way is the "better" way to do it. The best thing to do is for each individual to follow what was taught them by their Rebbeim/parents. If no such minhag exists, a competent Rav should be consulted.
That being said, if someone follows all the Minhagei HaGra (not just the easy ones, like having extra time for Sof Z'man Krias Shema) they should probably follow the Gr"a in this as well.
Our holy sages, the Chazal tell us תנא דבי אליהו כל השונה הלכות בכל יום מובטח לו שהוא בן עולם הבא, שנאמר הליכות עולם לו, אל תקרי הליכות אלא הלכות - one who studies [at least two] Halachos daily is assured a portion in Olam Haba - the world to come. (:מגילה כ"ח )