George Anton Kiraz's A New Syriac Primer is very student-friendly and has an audio component, which is helpful. This uses the Western Syriac pronunciation, which is unusual in most English-language textbooks.
I learned from Robinson's Paradigms and Exercises in Syriac Grammar; it uses the Western Syriac script, but the Eastern pronunciation. This is a weird convention Western scholars decided on.
Both books are really over-priced, the latter especially so, given its cheap glue binding. Wheeler M. Thackston's Introduction to Syriac is much more affordable, and not bad. It emphasizes reading without vowels, which is a pain at first but good in the long run. However, it uses both Eastern pronunciation and the Estrangela script. The scripts aren't THAT different, so that may be overblown as an impediment.
I would lean toward using Kiraz's book if I were starting today, especially if West Syriac sources are my goal.
