Suggestions are like weak advice when you use the modals could and might.  The verb that follows must be in the simple form.  Compare the following:

You must go see the dentist.  (the strongest advice)

You have to go see the dentist.  (the strongest advice)

You’d better go see the dentist.  (strong advice)

You should go see the dentist.  (regular advice)

You ought to go see the dentist.  (regular advice)

You could go see the dentist, if you wanted to.  (weak advice, more like a suggestion)

You might consider seeing the dentist.  (weak advice, more like a suggestion)

More examples with could and might:
You could apologize to her for forgetting your anniversary.
You could come early and help me set up the room.
You could take her to a movie for your first date.
You might try listening more carefully next time.
You might consider taking guitar lessons.
You might want to change your clothes before you go out.

When there’s nothing better to do that you can think of, use might as well or may as well.

Examples:
You might as well stop now and continue in the morning.  (You think it’s the best thing to do)
You may as well start over from the beginning.   (You think it’s the best thing to do)

Other ways to make suggestions:

Why don’t you/we/I is a question and is followed by a verb in the simple form.

Examples:
Why don’t you go clean up before dinner?
Why don’t we finish this first and then go eat?
Why don’t I make a reservation for this evening?

How about (also pronounced how ’bout) is a question and is followed by a gerund or if plus a subject and verb.

Examples:
How about going to the movies tonight?
How about if we go to the movies tonight?

How about learning how to drive?
How about if you learn how to drive?

Let’s and shall we are used when you include yourself.  Shall we is a question.

Examples:
Let’s take a break and go for lunch.
Shall we take a break and go for lunch?

Let’s get out of here.
Shall we get out of here?

NOTE:  Let’s = let us

Study this page and when you think you’re ready, do the following exercise.