Here I prefer the technique of Systematic Sampling where one selects every kth individual from the population. Thus, from a list of n arrived tweets, every kth tweet is chosen to construct a sample set of 's' tweets, such that k*s is close to n.
Advantages:
Simple statistically valid procedure
Accurate
Easier to implement and verify the correct tweets have been selected
Unbiased and representative, even more likely so than a Simple Random Sampling scheme, in the current context as this also sorts by time of arrival, where the latter criteria is likely material, as it spreads the sample over the day. As such, it can, for example, likely isolate workers, largely inactive 9 AM to 5 PM day, versus non-workers including students active 3 PM - 8 PM (after school), and older adults active latter in the evening.
Thus, the application of simple, easy to implement, unbiased and representative Systematic Sampling here likely also results in a spread of the sample over important age demographics and income classes.
Note: How one arrives at the best sample size 's' is an important topic, best discussed separately.
[EDIT] An important point that is duly noted by this educational reference, to quote:
You don't have a complete list, so simple random sampling doesn't apply...
So, technically the employment of a simple random sampling scheme, to assess characteristics of the parent population, is valid when one has a complete list of the population over which to subsample. This is NOT the case with a continuous occurring series of generated tweets constituting a subset of the tweeting universe. So, inferences on the parent population and, in particular, the very question as to whether it is representative of the 'whole sample', implying the parent population, only arguably can be answered here by a simple random sampling scheme. However, the same source does affirm the validity of systematic sampling in such a context, to quote:
Since we don't have access to the complete list, just stand at a corner and pick every 10th* person walking by.
*Of course, choosing 10 here is just an example. It would depend on the number of students typically passing by that spot and what sample size was needed.