If you just want to store it somewhere so MATLAB can work with it; pick your choice from the databases supported by matlab and then install the appropriate drivers for Python for that database.
All databases in Python have a standard API (called the dbapi) so there is a uniform way of dealing with databases.
As you haven't told us how to intend to work with this data later on, it is difficult to provide any further specifics.
the idea is that i wish to essentially download all of the data onto
my machine so that i can operate on it locally later (run analytics
and perform certain mathematical operations on it) instead of having
to call it from the server constantly.
For that purpose you can use any storage mechanism from text files to any of the databases supported by MATLAB - as all databases supported by MATLAB are supported by Python.
You can choose to store the data as "text" and then do the numeric calculations on the application side (ie, MATLAB side). Or you can choose to store the data as numbers/float/decimal (depending on the precision you need) and this will allow you to do some calculations on the database side.
If you just want to store it as text and do calculations on the application side then the easiest option is mongodb as it is schema-less. You would be storing the data as JSON - which may be the format that it is being retrieved from the web.
If you wish to take advantages of some math functions or other capabilities (for example, geospatial calculations) then a better choice is a traditional database that you are familiar with. You'll have to create a schema and define the datatypes for each of your incoming data objects; and then store them appropriately in order to take advantage of the database's query features.