Giving recommendations and pieces of advice

In communication we often ask for advice but more than asking, we like sharing our own opinion and offering a piece of advice to others. You can use a simple phrase "Я советую тебе..." [Ya sav'etuyu tibe] (I advise you...) for that in all cases. But if you are already good at Russian, you would probably want to make your speech richer and more diverse and use all linguistic tools. There are some constructions for that which express a piece of advice but at the same time they have stylistic difference (i.e. it's very important to find out who is speaking and whom we are addressing to in order not to be rude). Here are these constructions.

The first group is an advice-suggestion. It's not a strong recommendation; you rather share your opinion. You can use it among your colleagues as well as friends.

Может быть, + местоимение Д.п. + инфинитив СВ - Maybe + pronoun in Dative + infinitive in perfective aspect
А что если + местоимение Д.п. + инфинитив СВ - What if + pronoun in Dative + infinitive in perfective aspect
А не + инфинитив СВ + ли + местоимение Д.п. - Why don't + infinitive in perfective aspect + pronoun in Dative

Может быть, вам решить эту проблему завтра? - Maybe you will solve this problem tomorrow?
А что если нам отказаться от этого проекта? - What if we abandon this project?
А не поужинать ли нам в этом ресторане? - Why don't we eat at this restaurant?

The second group is a stronger piece of advice. You can use it in conversation with your parents, children or friends.

Не пойти ли + местоимение Д.п. + инфинитив СВ - Shall...go + pronoun in Dative + infinitive in perfective aspect
Может быть, + глагол 2л. буд.вр. - Maybe + verb in 2nd person, future
Пошёл бы + глагол 3л. прош. вр. СВ - Would...go + verb in 3nd, past, perfective aspect

А не пойти ли тебе погулять? - Shall you go for a walk?
Может быть, поешь? - Maybe you'll eat?
Пошёл бы почитал книгу - Would you go to read a book.