What are ways "common" and not so known to practice the first kind of proper giving?

How can "giving to one arriving (new)" be very practical and in many situations be done?

Where I live now, there is no Sangha -- but there are refugees and asylum seekers from other countries.

They tend to be homeless, jobless, perhaps don't speak the language. Sometimes (or in some countries) the country (i.e. the government) might have already accepted them as refugees, or sometimes their refugee claim will take months or longer to process.

The government can or will only do so much for them (e.g. receive asylum requests, issue temporary or permanent documents). Apart from the government, there some local organisation[s] of volunteers who try to help refugees -- find them a place to live (people who are willing to have them as guests, for few days or weeks or many months, until they can find a job and a place of their own), help them to apply for jobs, learn the local language, talk to government, get health care, food and clothing and so on, help with transport (e.g. driving), and school for any children.

Mental, verbal (signs) and physical?

If by that you're asking, "How does that happen?", I know how the local organisation started. There was (is) a man who speaks a foreign language, and who the government sometimes called to act as a translator when they interviewed a refugee.

Therefore he discovered the interaction between the government and refugees, and in particular that the government doesn't do everything to help refugees (or does more for some than for others), and that some refugees need help (e.g. are homeless).

When he retired he started an organisation of people to help refugees. And then, friends of these people find out -- e.g. your friend has a refugee couple staying in their home for months, you meet them and it seems alright, feasible, and you think "I could do that too" and you offer to try to help, and you meet someone from the organisation and they ask, "these people need a home, could you put them up for like three nights and see how it goes?" and if it works fine and it's supportable then you continue, and so on, lots of networking.

To some extent it's like ordinary guest-friendship, I guess, i.e. staying or visiting with people when travelling. My uncle (who in his youth hitch-hiked across Europe and the Middle East) once joked that, "I don't travel fro place to place, I travel from person to person."

Do you think it is not possible that a form of behavior might fall under two different categories? Both Dana and Sila? That both might encompass each other when seen from different perspectives?

Do you consider the gift of Dhamma (the best gift) and the gift of teaching to be two different things?

The idea of The Gradual Course is to provide a solid basis from which to expand one's knowledge and practice. Thus it is not intended to be absolutely comprehensive in depth, but only in scope. With that in mind I have provided numerous links to source material. The work should be regarded as a starting point and stimulus to further research, not a place where one will find one's work already done for one.

A general run-down of all aspects of the practice of Dana - the first step in the Gradual Course, the instructions usually given by Ananda to lay disciples - the very first steps that should be taken by a very beginning Buddhist are described here:

http://buddhadust.net/dhammatalk/the_pali_line/course/gradualdana.htm

In the list defining when to give, the first is to give to one arriving. That means when someone visits you or is new to an institution or neighborhood then it is a good time to make a gift to them. Welcome baskets, signing bonuses and so forth as well as the more basic: food, clothing, shelter and medicine that would be helpful to a visiting bhikkhu or for making good kamma giving what you would need in times of need.

But also of interest there: Who to give to, what to give, how to give, the best gift, repaying one's parents, etc. ... and then the rest of that Course.

The main problem with beginning Buddhists today: they want to start at the top, with jhana practice where what should be done first is the building of a strong foundation as described in this course. There is no attaining jhana without a platform based on giving, ethical behavior, self-control and organization of the mind as described in this course.