Should she marry a man who is religiously-committed but poor?

If this man is religiously-committed and of good character, there is nothing wrong with you marrying him, even if he is poor, because of the report narrated by al-Tirmidhi (1084) from Abu Hurayrah (may Allaah be pleased with him), that the Prophet (peace and blessings of Allaah be upon him) said: “If there comes to you one whose religious commitment and character pleases you, then marry [your female relative who is under your care] to him, for if you do not do that, there will be tribulation on earth and much corruption.” Classed as hasan by al-Albaani in Saheeh al-Tirmidhi. 

There is nothing wrong with him taking from your wealth with your consent, and you will have the reward for spending on him and treating him kindly. Allaah says (interpretation of the meaning): 

“but if they, of their own good pleasure, remit any part of it to you, take it, and enjoy it without fear of any harm (as Allaah has made it lawful)”

[al-Nisa’ 4:4]

Poverty is nothing to be ashamed of, because wealth comes and goes, and a poor man may become rich. Allaah says (interpretation of the meaning): 

“And marry those among you who are single (i.e. a man who has no wife and the woman who has no husband) and (also marry) the Saalihoon (pious, fit and capable ones) of your (male) slaves and maid‑servants (female slaves). If they be poor, Allaah will enrich them out of His Bounty. And Allaah is All‑Sufficient for His creatures’ needs, All‑Knowing (about the state of the people)”

[al-Noor 24:32]

You should convince your mother, and explain to her that compatibility is not the matter of money, rather it is piety and righteous deeds. There is no sin on you even if your mother persists in her view, and you think that you want to marry him, but it is essential that your wali (Guardian) be present in order for the marriage to be valid, because the Prophet (peace and blessings of Allaah be upon him) said: “There is no marriage without a guardian.” Narrated by Abu Dawood (2085), al-Tirmidhi (1101) and Ibn Maajah (1881), from Abu Moosa al-Ash’ari, and classed as saheeh by al-Albaani in Saheeh al-Tirmidhi. 

The woman’s guardian may be her father, then her son, then her brother, then her nephew (brother’s son), then her paternal uncle, then her cousin (son of paternal uncle), in order of closeness. If she does not have a guardian then her guardian for marriage is the qaadi (judge), because the Prophet (peace and blessings of Allaah be upon him) said: “If they dispute, then the ruler is the guardian of the one who has no guardian.” Narrated by Ahmad (24417), Abu Dawood (2083), al-Tirmidhi (1102); classed as saheeh by al-Albaani in Saheeh al-Jaami’ (2709). 

If a woman strives to get married and makes the mahr easy, it is a sign of wisdom and good thinking on her part. We ask Allaah to make things easy for you and to guide you to the right path. 

And Allaah knows best.