I know that Aramaic was written two scripts; its original alphabet (which is today's Hebrew script) and the Syriac script. What script would Jews have used to write it in the 1st century? Were both scripts in use in different parts of the Middle East?
For Jews in the 1st century, it would've been the Aramaic block that's also today's Hebrew (and Hebrew in the 1st century, too). The font has changed somewhat over time, but is still recognizable. For some examples, have a look at this bit of the Dead Sea Scrolls.
However, in other parts of the Middle East other scripts might be used. Nabatean used a script that's a bit reminiscent of Arabic (and historically, it is related to it). Here's an example. The Syriac script (or an early version of it) would've been used in other areas, too, but I don't have any examples handy.