settle down to + verb or gerund?
It seems that the phrase "settle down to" can be followed by a verb, a gerund, or a noun.
For example:
1. Thus we can all settle down to making money again. (gerund)
2. After lunch the children settled down to finish their science projects.(verb)
3. Let's settle down to business.(noun)
4. Let's settle down to work. (a verb or a noun?)
My question is:
1. Do they all grammatically natural to you?
2. Which grammar form do you prefer?
3. Let's settle down to "work," a noun or a verb?

Question

settle down to + verb or gerund?
It seems that the phrase "settle down to" can be followed by a verb, a gerund, or a noun. 
For example:
1. Thus we can all settle down to making money again. (gerund)
2. After lunch the children settled down to finish their science projects.(verb)
3. Let's settle down to business.(noun)
4. Let's settle down to work. (a verb or a noun?)
My question is: 
1. Do they all grammatically natural to you? 
2. Which grammar form do you prefer? 
3. Let's settle down to "work," a noun or a verb?

Answer

All the sentences are correct but for different reasons.

The basic phrasal verb is "to settle down". It has no direct object.

You can "settle down (in order) to do something". Here, "to" is part of an infinitive of purpose. This is the same construction that would be used for any verb e.g. I moved house (in order) to be closer to my work.

In the construction, settle down + to + noun/ing, "to" is a preposition. Prepositions are always followed by nouns, noun phrases or an -ing (gerund).