I've got a Stevens 200 in .223. I took the original stock off earlier and the mag went with it. That means it's a center feed correct?

How do I determine if it's a short or long action. My assumption is that it's short but that's only because I'm shooting a small caliber.

I measured the distance between the action screws and it seems to be around 4 3/8 - 4 7/16

Finally, with my limited knowledge I determined that this is what I need http://www.boydsgunstocks.com/Produc...alnut-finished
With the details I've given, does this seem correct?

One more question, will the new stock come with a new mag so that's it's no more than a simple drop in or will I have to somehow get the mag out of the original stock and put it in the new one. If I have to put the old mag in the new stock, are there any tutorials on how to do so?

Thanks in advance for the help!