Right understanding of Dāna

Karma in giving is the product of the state of the mind of the giver and the recipients. If we give something in earnest and the recipient is not then the merit is diminished similarly when we do not have a strong volition but the recipient is overjoyed. The most merit results when the giver has strong volition and the recipient also has great appreciation.

Also pure and focused the mind greater the volition and appreciation.

So people in need getting something they need is means the recipient will appreciate it more and would result in better results. Rich or poor you should help at the hour of need.

Also helping people with pure mind like meditators will give better results.

The Buddha spent was amount of time to set establish the Sasana so anything inline with the Buddhas efforts and will brings great merit hence that is why donation to the Sangha is more meritorious than the personal donation to a Buddha.

Householder Robin, interested,

aside of the already given answers, in relation to "Is there a general concern for the (unworthy) poor in Buddhism?"

Giving as part of training upwardly and beyond has release and freedom as it's purpose and only dependency and indebting toward liberation. Where ever one gives into, nourishes it, by deeds, word and thoughts, grows for one, inwardly and outwardly. Where ever one does not give into, dies for one, inwardly and outwardly. Now would a wise person like Sublime or lower growing for him?

There are five proper occasions for placing ones generosity, outside of giving that is a duty in ones relationship one nourishes on (which falls under Sila, virtue, and its violation, actually):

"There are these five seasonable gifts. Which five? One gives to a newcomer. One gives to one going away. One gives to one who is ill. One gives in time of famine. One sets the first fruits of field & orchard in front of those who are virtuous. These are the five seasonable gifts." Kaladana Sutta: Seasonable Gifts

What ever gifts are given outside this proper seasons, and not really related to duty, naturally increase attachments, bounds and problems.

The Buddha and wise generally encourage to give into better, higher and more Sublime at first place for fast growing. Maintain ones duties within equal one dwells and to place out of compassion and in proper situations, if possible also toward those behind.

Giving downward is very popular and modern (actually mostly business and trade for livelihoods, what is sold as de-velopment, for the most is actually en-velopment, making dependend, mostly even with strategies to win over), since one easier gains a state of feeling good and superior and such giving also makes receiver easy bond to one. So for the most such giving seeks interest and amassing in the world, makes others depended on one and in debts. As for those in lower positions it's better if guiding and giving toward doing merits and conduct causes for own future well-being as to serve possible useless desires aside of needed. That is also why the gift of Dhamma excels all other gifts. Maybe good to note here that every being, even the most bad, is worthy of being supplied to live on, with food, medicine and space for such.

See also Vaccha Sutta: To Vaccha and Dana, Caga - Generosity

Possible also important to note is, that it's usual and good, if one likes to help others bond in relations, to always give first the leaders, parents, preceptors of those "poor" are bond to, since if the relations are broken and disturbed by improper giving (causing unwise to think that they now can do as they wish), such destroys not only families but even nations, which is also often very systematical used for the sake of causing degeneration and by all unwise actions on wrong view, causes may troubles in this world and imbalance in relations, wars and detaching from any way upwardly for many.

(Note that this Dhamma gift is not given for trade, exchange, stacks, entertainments to bind or conduct demerits with it, but for release from this wheel)

In Buddhism the merit created is greater if you give food to a monk when compared with giving to a prisoner for example, it doesn't mean you should not help the prisoner, it means that you create more merits by helping pure and enlighted beings to survive, there are many stories on the dhammapada about it.

Think as if you are helping the Sangha to survive, so they can benefit inumerous beings, the impact in the world is bigger and so the merit earned.