At the risk of appearing old-fashioned, it is certainly acceptable to use a colon to introduce a list split across sentences. Just be sure to start the first sentence with a capital letter:
We required three ingredients: Firstly, eggs, to provide a nice eggy flavour. Secondly, milk, for all its milky goodness. Finally, we required flour, to bind it all together.
In modern writing, first and second are preferred. The full-stops (or periods) would also give way to semi-colons:
We required three ingredients: first, eggs, to provide a nice eggy flavour; second, milk, for all its milky goodness; finally, we required flour[,] to bind it all together.
For succinctness, first, second and finally, we required are best removed, as they make the whole sentence rather wordy. Thus:
We required three ingredients: eggs, to provide a nice eggy flavour; milk, for all its milky goodness; and flour, to bind it all together.
You may notice I played around with the commas. That could also be considered a matter of style, but I tend to be fastidious with regard to comma punctuation.
Punctuation is a matter of style, and as such you should be guided by your manual of style. I use the Chicago Manual of Style, which advises as follows:
Use a semicolon to indicate a break in thought larger than that indicated by a comma, especially between independent clauses when a conjunction is omitted.
Use a colon 1) to indicate a break in thought larger than that indicated by a semicolon but smaller than that indicated by a period, especially between two clauses the second of which explains, illustrates, or amplifies the first or 2) to introduce a list of items that do not form a complement or an object in a clause.
So first you have to decide whether CMS is an appropriate reference. If you decide that it is, you then have to decide what you're trying to say. Are you explaining your project goals in a closely related clause? If so, then write
There are two goals I want to accomplish; I want to make it more
efficient and give it more exposure.
This is in place of writing, "There are two goals I want to accomplish, and they are to ...."
If you're listing a set of goals then write
For this project, I have two goals: make it more efficient and give it more exposure.*
Notice that per the colon rule part 2, you would not write
For this project, my two goals are: make it more efficient, and give it more exposure.
* Omit the comma between the compound phrases
Best Answer
There are actually 5 examples of colon usage in your question. All three that have the word "example" before them are Ok.
Here is a short list of rules on how and when to use colons.
But the punctuation after the name "David" should be a comma instead. This is because you are using "direct address." This is also true in business writing and an email.