I have various Syriac grammars and other works. Many resources can be quite expensive, as they are meant for scholars and specialists, but some of the older works have been reprinted recently and cheaply via self-publishing venues like lulu.com, such as Rev. Thomas Arayathinal's misleadingly-titled two volume "Aramaic Grammar" (which teaches Syriac, not Aramaic). Something like that might be a good bet to get the basics, if you don't want to spend $75-$100 minimum on Gorgia's Press materials (though I have heard good things about Kiraz's Intro to Syriac, published by Gorgia's and actually available right now on Amazon for a bit less than that; I've never actually used it myself, though). I know that Noldeke's grammar has been reprinted, too (as part of the Ancient Language Resources series that also gave us the reprint of Crum's epic and still unequaled Coptic dictionary), and I would figure that this is probably worth owning if you're serious about learning from standard references.
(I only put the bit about "standard references" in because I have noticed that there are a lot of books you can find on Syriac that are pushing a certain agenda vis-a-vis Syriac primacy and even sometimes some weird theological ideas, too -- i.e., the works of Lamsa and his students like Rocco A. Ericco and others. I actually have one of Errico's books myself, only because it was the cheapest option at the time that also came with audio recordings, but I don't use it very much because the audio recordings are of poor quality. Anyway, you shouldn't need to put up with any weird nonsense just to learn the basics of the language.)