You should be fine using the Streaming API unless these ~ 1000 users tweet more (very) approximately 60 tweets per second at any time.
Using the statuses/filter streaming API endpoint with the follow parameter, you can use up to 5000 users. There is a speed limit, unless the stream returns more than 1% of all tweets that are currently being tweeted. (60 tweets per second make up 1% of the average tweet rate, which always fluctuates, so don't rely on this number.)
If your flow exceeds 1% of the threshold, you may find this. (Pay attention to LIMIT .) Then you should use the REST API to search for missing tweets.
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