Is the Syriac Aramaic Peshitta valuable for reading Jesus's words, and did He speak Aramaic?

Here is the thing: we do not actually know what language Jesus spoke. We think he spoke Aramaic, but that is not a proven reality; Jesus could very well have spoken Greek. Greek was the universal language of the world from about 300 BC onward, and Latin came from Greek; Aramaic was a diluted form of Hebrew, and while any Jew would understand it as he understood Hebrew, if you were going to survive and do business in that world you had to know Greek. There are a few Aramaic phrases in the New Testament, like talitha koum when Jesus told the little girl to rise, but they are very rare, so whether Jesus habitually spoke Aramaic is an open question. That said, any early translation like the Peshitta will give you insights, because those people lived closest to that time and were familiar with the culture, the idioms, and the connotations of words far better than we are, so you will inevitably find some illumination from it.