/ Do I need a work visa before moving to Poland?
My experience of going through the Warsaw airport (nervously) with no visa or permit of any kind: worker at the desk says "Proszę dokumenty", glances at my passport, stamps it, and waves me off, and I'm safe in Poland. That's it.
If you're an American, you can stay up to three (3) months in Poland (in the whole EU Schingen Area actually) with no visa or anything, just as a tourist. So, what you can do is you can come to Poland with no visa or permit or anything, and then apply for a residence permit (at your local urząd wojewódzki - Polish government province office) once you get here. That's what I did.
The important thing is that you have a valid reason for staying, like work or studying. I'm a student at the University of Wrocław, so that's a legitimate reason in the eyes of the government. I don't know what is necessary for your work to qualify you to stay, though. But if your company says they'll see to it that you get the work permit, then I guess you're good.
Just make sure you start on the process before half of your three month period is up (i.e. 45 days in at the latest), but preferably as soon as you can once you get to Poland, because they really take their time about it at the government office. Otherwise, you may get a call 5 days before your 3 months are up, telling you that you have to take a weekend trip to Ukraine and spend the night there, in order to give them more time to process everything. That almost happened to me, and it did happen to another American friend of mine.
(Actually, I think the official rule is that, after your free 3 months have expired, you have to spend 180 days outside of the Schingen area before you can come back in for another 3 months. But if the Polish government is okay with me just spending the night in Ukraine [actually later they even said Germany or the Czech Republic would be okay], then I won't say anything! It seems strange to me that one government can give you an exception for the whole Schingen area though.)
It all sounds kind of scary, and as an American you do have to go through a lot of annoying documentation compared to EU residents, but also as an American you don't really have to worry about anything going too horribly wrong, I don't think.
As for what everyone's saying about money, I don't know what expenses are like in Kraków exactly, but I do know it's pretty expensive. Poland is generally cheap for an American, but when I was walking through the streets of Kraków looking at restaurant prices, I almost felt like I was in a big American city. They may just be taking advantage of tourists in those restaurants, though.
Is your language school providing a place for you to stay? I know TEFL offers an internship starting in February for teaching English, and I think they provide accommodation and a (albeit small) spending allowance. I'm not sure what their education requirements are but maybe you could check it out:
Anyhow, I think your situation might be doable, but if I were you I would offer private English lessons on the side to supplement your income. So you should probably start learning Polish, if you haven't already, to make that easier for you. Just be determined. It won't be easy, but you can accomplish anything if you put your mind to it. ;)