1. 表示“建议”时，propose 跟suggest 用法一致：

（1）propose that...(should) ...

（2）propose doing

2. 表示“想要做某事”，propose 有intend 之意。这时，propose doing 和 propose to do 都对。

你的这两句话：第一句有两种意思（1.建议；2.想要）；第二句只有一种意思（想要）

She proposed catching the early train. 

她建议赶早班火车。

她想要赶早班火车。

She proposed to catch the early train. 

她想要赶早班火车。

3. 在日常会话中，可以说：

propose that + 一般现在时

I propose that Ms Hallam is appointed.

以下内容来自《朗文词典》：propose

▲propose = SUGGEST [transitive] formal to suggest something as a plan or course of action → proposal

 The changes were first proposed last year.

propose (that)

 In his speech he proposed that the UN should set up an emergency centre for the environment.

propose doing something

 The report also proposes expanding the airport.

▲propose = INTEND [transitive] formal to intend to do something

propose to do something

 How does he propose to deal with the situation?

propose doing something

 We still don’t know how the company proposes raising the money.

▲ GRAMMAR: Patterns with propose

• In everyday English, you propose that someone does something:

I propose that Ms Hallam is appointed.

• In more formal English, you propose that someone do something, using the base form of the verb (=infinitive without ‘to’):

I propose that Ms Hallam be appointed.

✗Don’t say: I propose Ms Hallam to be appointed.

• You can also use the base form when talking about the past:

I proposed that Ms Hallam be appointed.

• You propose that someone should do something:

He proposed that we should have another meeting.

This pattern is used especially in British English.

• You say it was proposed that someone (should) do something:

It was proposed that we (should) have another meeting.