Charlotte’s decision to accept Mr. Collins is financially prudent because they will have supportable income. To me the financial prudence of Charlotte’s marriage is indisputable but the question of whether she chose the right man is disputable—they are two separate issues however and I do not lump them together. I daresay there have been times when people do meet and establish a lasting happy relationship in days so that alone is not enough for me to say her choice of Mr. Collins is rash. I think Charlotte considered several factors including fortune before deciding to secure Mr. Collins:

"Well," said Charlotte, "I wish Jane success with all my heart; and if she were married to him to-morrow, I should think she had as good a chance of happiness as if she were to be studying his character for a twelvemonth. Happiness in marriage is entirely a matter of chance. If the dispositions of the parties are ever so well known to each other, or ever so similar before-hand, it does not advance their felicity in the least. They always continue to grow sufficiently unlike afterwards to have their share of vexation; and it is better to know as little as possible of the defects of the person with whom you are to pass your life." (Chapter 6)

First, I think Charlotte consults her own feelings on men and marriage and pursues a course which she feels offers the best chance for her happiness—the same course she outlines in Chapter 6. There is no rule that Charlotte must have the same standards for a husband and marriage as Lizzy and Jane. Charlotte’s standards are very different from theirs; in Chapter 6 Lizzy does not persuade Charlotte to see the error of her ways or visa-versa and they both continue to adhere to their own philosophies. Charlotte feels that after marriage couples inevitably grow unlike each other so the agreeableness of a husband at the start of the marriage does not matter; in her opinion if he starts out as agreeable eventually he would become less so causing vexation. I can only suppose this is an opinion she has formed watching the marriages around her. When she says she is not romantic IMO she means two things. She does not think she needs romantic love to be happy and she does not believe in the ideal marriage where partners love each other, enjoy each other and grow closer as the years go on. Charlotte believes because of her unromantic nature that she will be able to be happy in a marriage that is less than ideal with a man she does not respect or esteem.

…marriage had always been her object; it was the only honourable provision for well-educated young women of small fortune, and however uncertain of giving happiness, must be their pleasantest preservative from want. This preservative she had now obtained; and at the age of twenty-seven, without having ever been handsome, she felt all the good luck of it. (Chapter 22)

Second, I think Charlotte takes into account her situation in life. Her brother’s worries in Chapter 22 that she would be an old maid is probably one she had herself and she may feel Mr. Collins is her last opportunity. Charlotte has weighed her future options other than marriage. She obviously feels marriage, even to Mr. Collins is preferable to spinsterhood or other “dishonorable” means of preserving herself such as working in some capacity. I think JA did not have to detail these options because her contemporaries would know that women of little fortune without connections or great beauty or accomplishments have little by which to attract a husband other than their character and domestic felicity which sadly seems to have not been noticed by any gentleman in Charlotte’s case.

Mr. Collins's character, connexions, and situation in life, I am convinced that my chance of happiness with him is as fair as most people can boast on entering the marriage state." (Chapter 22)

Third, Charlotte considers Mr. Collins’ situation in life. He is respectable, he has a job for life, will inherit Longbourn and he has good connections. Marriage to Mr. Collins secures her a future as a respectably married woman and raises her status.

The stupidity with which he was favoured by nature must guard his courtship from any charm that could make a woman wish for its continuance…Mr. Collins, to be sure, was neither sensible nor agreeable; his society was irksome, and his attachment to her must be imaginary. (Chapter 22)

Fourth, Charlotte considers Mr. Collins character. She thinks he is stupid and weak minded and unable to distinguish emotions in others and so far incapable of very deep feelings for any woman—he goes from Lizzy to Charlotte quite happily. She may have felt he was just the right sort of man for her plan of securing a husband by showing more affection than she feels. She may have only met Mr. Collins four days prior to accepting him but she had her plan at least since Chapter 6 and the reasoning behind her plan shows she has held the opinion for quite a while. Since Charlotte is nearing spinsterhood, has a plan, does not think highly of men in general, is not romantic and she feels there is just as much a chance of happiness with Mr. Collins as most people can expect when they marry her decision to secure him quickly is not so surprising.

You do not make allowance enough for difference of situation and temper. (Chapter 24)