What's the idiomatic way to politely propose an activity?

Question

In English we have:

• Would you like do x?
• Should we do x?
• Let's do x

What would the idiomatic equivalent(s) in Russian be? For instance a literal translation of should we go to work? might be мы должны встретиться после работы ? (I used a translator here, my Russian isn't so good and Google is failing me on this issue.)

Even if this is literally correct, I doubt that it is idiomatic Russian, as in my experience, Russian phrases tend to be a little more direct/to the point.

A language learning site suggested:
Я хотела бы пригласить тебя к себе на ужин.
For I would like to invite you to dinner at my place.

Is that the same level of politeness as it sounds like it is in English?

Answer 1

The common patterns for translation of such questions are:

• [Pronoun] verb ... ?
• [Не] verb [ли] pronoun ... ?

Where optional parts are enclosed in brackets.

For example, the following questions have the same meaning Would you like to have a drink?:

Выпьем?
Хотите выпить?
Вы хотите выпить?
Не хотите выпить?
Вы не хотите выпить?
Не хотите ли выпить?
Не хотите ли вы выпить?

The first form is the most direct. The last one is the most politeness.
More words - more politeness. :)

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So the Russian equivalents are:

• Would you like do x?

  [Не] хотите [ли] x?
  [Вы] хотите x?

• Should we do x?

  [Не] должны [ли] мы x?
  Мы должны X?

  Or

  [Не] следует [ли] нам x?
  Нам следует x?

• Let's do x

  Давайте сделаем х?
  Сделаем x?

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The translations of

Should we go to work?

are

Мы должны идти на работу?
Не должны ли мы идти на работу?
etc

Answer 2

Even more polite would be:

Не хотели бы Вы выпить?