I seem to have read that the "original" or "oldest" Tripitaka was written in Pali, but at the same time the Sanskrit language is much older than Pali. How do Sanskrit and Pali relate in terms of Buddhism? I would like to collect as many Buddhist terms and their meanings in one of these two languages but not sure which would provide the deepest, most concise, clear, and complete terminology for the Buddhist cosmology and theories of mind and such. Sanskrit seems like it has a richer more established etymological system so it might be easier to understand concepts that way, but perhaps Pali is closer to the original meaning or something? Which language would be better for a beginner or advanced student of Buddhism?
Vedic Sanskrit is much older than Pali. Pali part of the family of Prakrits which descended from Vedic Sanskrit. The Buddha spoke a Prakrit dialect. Jain scriptures too were written in some kind of Prakrit dialect.
Classical Sanskrit was standardized by the ancient grammarian Panini around the same time as the lifetime of the Buddha. It too descended from Vedic Sanskrit. When we say Sanskrit today, we mean Classical Sanskrit.
Vedic Sanskrit is analogous to Old Latin. Prakrit is analogous to Vulgar Latin. Pali is analogous to Italian. Classical Sanskrit is analogous to Classical Latin.
Pali is a lot simpler than (Classical) Sanskrit in the sense that its grammar rules are simplified. For e.g. for nominal noun declensions, Sanskrit has three - singular, dual and plural. Pali only has two - singular and plural.
Words are simplified too. For e.g. maitrī → mettā, sthavira → thera, tṛṣṇa → taṇha, smṛti → sati.
Sanskrit is also a grand literary language and formerly a lingua franca in the Indian subcontinent, just as Latin was in Europe. It was the language of the royals, the clergy and the poets.
Prakrit dialects were used by the common people and the Buddha preferred his teachings to be spread in the language of the common people. Pali is a kind of standardized Prakrit used for the standardization of the Pali Canon.
Pali is only used in the Pali Canon and its commentaries or related works like the Visuddhimagga.
Then there's one more language called Buddhist Hybrid Sanskrit (BHS) which is a hybrid dialect, between Pali/ Prakrit and Sanskrit. It's largely used by early Mahayana scriptures. Later Mahayana scriptures were composed in Classical Sanskrit because that became the main written language when people started writing.
So, which language will get you deeper into Buddhism?
That depends on which scriptures or texts you want to read.
In any case, Pali and Sanskrit are very similar. Think of Sanskrit being like German and Pali being like English, a Germanic language with much simpler grammar (but let's forget the large amount of Latin loan words). And BHS is something in between the two, like Dutch.
It really depends on what kind of Buddhism you practice. For example, if you practice in a Thai forest tradition, being familiar with the technical Sanskrit jargon of the Yogacara school would be completely irrelevant. Likewise if you were a student of Zen, being able to read the Tibetan tantras would be a complete waste of time. I'd argue that there's definitely more written in Sanskrit, but even within that literature there will be texts that in no way influence how you practice.
FWIW, Pali isn't that hard of a language to learn...especially if you already speak a language that uses noun declensions. Structurally, Sanskrit is very, very similar - just with a couple of extra cases. One thing I will say, however, is that there are vastly more resources for learning Sanskrit. That alone will probably make it easier to pick up.
If you want to learn Therawada Buddhism, learn Pali Language. Sinhalese (Sri Lankan native) is also a good language to learn Buddhism as there are a lot of Pali text translated to Sinhalese and there are a lot of Sinhalese monks who can help you understand Buddhism.
I might be biased, but I find it quite difficult to express Dhamma in English as there are too many subtle but important points either missed, misinterpreted or misunderstood. You are learning the physics of the mind, which could be thought of as the most complex thing. Language clarity is quite important.
Academically: English, Japanese, Chinese, French, and German. There is a lot more Japanese scholarship on Buddhism than English, a lot more Chinese scholarship as well. Many of the early groundbreaking translations of the buddhavacana into Western languages were by Frenchmen in the late 1800s, such as de La Vallée-Poussin et al.
On terms of practice, if you want to familiarize yourself with the texts, I would say the same as other users, adding Chinese and Tibetan to the list of languages to learn depending on what tradition you are most interested in and which manuscripts you think would be more interesting. They are very difficult languages for non-specialists to learn, but if you learnt Tocharian or Gāndhārī, you'd be one of very few people with access to a host of very old Buddhist manuscripts.
I will say, based on the precedent of Franklin Edgerton's paper "The Prakrit Underlying Buddhistic Hybrid Sanskrit" (which is very generously cited in Wikipedia's page on "Buddhist Hybrid Sanskrit"), that Buddhist Sanskrit can be quite distinct from both Vedic and Classical Sanskrit. According to the cited text, when Buddhist Sanskrit significantly differs from Classical Sanskrit, it retains word senses and meanings largely identical to Pāli (see p. 502 of the cited paper). So it might actually be significantly more useful to learn Pāli instead of Vedic or Classical Sanskrit. There do exist courses in Buddhist Sanskrit, but they are rare. Here is one:
You could look for courses like that if you've a fancy for obscure Buddhist Sanskrit. Buddhist Sanskrit, however, is more like Pāli than it is like Vedic or Classical Sanskrit.