1. The construction company offered us the new houses.
2. My friend suggested that we spend Christmas together.
3. The menu offered us a wide choice of sweets.
In the US, "propose" is used primarily with more formal things, to include business items.
a. We will be meeting so he can give me his proposal for the new building.
b. We will propose a whole new way of doing things at the coffee shop.
When I think of "offer" vs "suggest, an "offer" is usually a physical thing, while a suggestion is a verbal thing. You physically offer something, you verbally suggest something.
a. He offered her a drink. (Even though he might have only stated it, in your mind, you can picture him physically holding drinks out on a tray.)
b. He suggested she choose the red wine. (This would be a verbal statement.)
Also:
1. The construction company offers us the new houses. 2. My friend suggested we spend Christmas together. 3. The menu offers us a wide variety of sweets. Thank you very much!
The use of the verb "offer" is mostly used that they give you a gift. Like "My friends offered me a trip to Vegas" or "I didn't get the job I wanted, but they offered me another job they thought I would like".
The use of "suggest" is to give an option of what someone can or should do. "I suggest you take a trip to Vegas" or "I suggest you try to apply for another job".
The use of "propose" is kind of similar to suggest, but I think it may be more formal. "My friends proposed bringing me to Vegas", "I couldn't get the job, so they proposed I tried applying for a similar job"
