Archiving Tweets via Python
The code is more 'Pythonic' than the majority of the codes I have seen here. Are you sure you are just a beginner in python?

One suggestion is to keep consumerKey, consumerKeySecret, accessToken and accessToken secret in another python file, and import these values from that file.
If you do that then, when you need to send this code to somebody or upload it anywhere, you can do it without worrying about making your consumerKey, consumerKeySecret, accessToken and accessToken values public.

Some of your lines are too long. I recommend you to follow PEP 8 standards while writing the code.

Also keep the naming convention uniform throughout the code.If you are using camelcase, then follow camelcase throughout.

I believe that you can do the following task

for tweet in reversed(tweets):
    latestID = tweet.id_str


like this:

lastID = tweet[0]


Also you are appending the tweets into a file and get_last_id() returns the topmost tweet id. I think that is a bug.

A class for each Tweet would have been better. That will make the code more beautiful.

Here is my implementation: github. You can refer it while converting this into a class. 
PS: My code is also not perfect. So I also welcome any comments, tips on my code too.