As of February 2, 2018, Twitter offers access to their full archive of tweets on a monthly basis, creating a less costly option than the enterprise API. The blog post introducing the premium full-archive search option has some details and links, or you can take a look at the per-month pricing. There are other options for purchasing access to tweets, and we recommend looking at Social Feed Manager's "Where to get Twitter data" guide for links to such services and other useful resources.
Below are links to a few tweet ID datasets that are freely available online, though some strategic Internet searching may yield other options. In order to acquire tweets from the Twitter API based on these saved tweet IDs, you'll need to make use of a tweet hydrator, such as Documenting the Now's Hydrator.