Conditions of Wali (Guardian) in Islam
Question

What exactly constitutes a guardian, as is needed in the marriage ceremony. I am a female Muslim, and I want to know if my older brother is acceptable for this role.
Praise be to Allah.Pillars of marriage in Islam
There are three pillars or conditions for the marriage contract in Islam:

Both parties should be free of any obstacles that might prevent the marriage from being valid, such as their being mahrams of one another (i.e., close relatives who are permanently forbidden to marry), whether this relationship is through blood ties or through breastfeeding etc., or where the man is a non-Muslim and the woman is a Muslim, and so on.
There should be an offer or proposal (ijab) from the wali or the person who is acting in his place, who should say to the groom “I marry so-and-so to you” or similar words.
There should be an expression of acceptance (qabul) on the part of the groom or whoever is acting in his place, who should say, “I accept,” or similar words.

Conditions of marriage in Islam
The conditions of a proper marriage contract are as follows:

Both the bride and groom should be clearly identified, whether by stating their names or describing them, etc. 
Both the bride and groom should be pleased with one another, because the Prophet (peace and blessings of Allah be upon him) said: “No previously-married woman (widow or divorcee) may be married until she has been asked about her wishes (i.e., she should state clearly her wishes), and no virgin should be married until her permission has been asked (i.e., until she has agreed either in words or by remaining silent).” They asked, “O Messenger of Allah, how is her permission given (because she will feel very shy)?” He said: “By her silence.” (Reported by al-Bukhari, 4741)
The one who does the contract on the woman’s behalf should be her wali, as Allah addressed the walis with regard to marriage (interpretation of the meaning): “And marry those among you who are single…” [al-Nur 24:32] and because the Prophet (peace and blessings of Allah be upon him) said: “Any woman who marries without the permission of her wali, her marriage is invalid, her marriage is invalid, her marriage is invalid.” (Reported by al-Tirmidhi, 1021 and others; it is a sound hadith)

The marriage contract must be witnessed , as the Prophet (peace and blessings of Allah be upon him) said: “There is no marriage contract except with a wali and two witnesses.” (Reported by al-Tabarani; see also Sahih al-Jami’, 7558) 
Conditions of the wali
The conditions of the wali are as follows:

He should be of sound mind
He should be an adult
He should be free (not a slave)
He should be of the same religion as the bride. A non-Muslim cannot be the wali of a Muslim , male or female, and a Muslim cannot be the wali of a kafir, male or female, but a non-Muslim can be the wali of a non-Muslim woman for marriage purposes, even if they are of different religions. An apostate (one who has left Islam) cannot be a wali for anybody.
He should be of good character (‘adalah – includes piety, attitude, conduct, etc.), as opposed to being corrupt. This is a condition laid down by some scholars, although some of them regard the outward appearance of good character as being sufficient, and some say that it is enough if he is judged as being able to pay proper attention to the interests of the woman for whom he is acting as wali in the matter of her marriage.
He should be male, as the Prophet (peace and blessings of Allah be upon him) said: “No woman may conduct the marriage contract of another woman, and no woman can conduct the marriage contract on behalf of her own self, because the zaniyah (fornicatress, adulteress) is the one who arranges things on her own behalf.” (Reported by Ibn Majah, 1782; see also Sahih al-Jami’, 7298)

He should be wise and mature, which means being able to understand matters of compatibility and the interests of marriage.
Order of who can take the role of the wali
The jurists put possible walis in a certain order, and a wali who is more closely-related should not be ignored unless there is no such person or the relatives do not meet the specified conditions. 

A woman’s wali is her father, 
then whoever her father may have appointed before his death, 
then her paternal grandfather or great-grandfather,
then her son, then his sons or grandsons, 
then her brother through both parents (full brother), 
then her brother through her father, 
then the sons of her brother through both parents, 
then the sons of her brother through her father, 
then her uncle (her father’s brother through both parents),
then her father’s brother through the father,
then the sons of her father’s brother though both parents, 
then the sons of her father’s brother through the father, 
then whoever is more closely related, and so on – as is the case with inheritance. 
The Muslim leader (or his deputy, such as a judge) is the wali for any woman who does not have a wali of her own.

And Allah knows best.