to know what model, use this link
http://www.appleserialnumberinfo.com/Desktop/index.php
be sure he does not give you the ethernet-ID or something other he thinks is the serial#
Why always recommend a SSD. First try normal SATA drives, you can still sell the SATA drive for a SSD, if you feel it would help you.
About DVD-R DL. Actually DVD-R DL is the standard for Apple drives, the older ones can not read/burn DVD+R DL. Some that can read/burn DVD+R DL have problems with some brands of DVDs (DVDs do burn, but stop at the Dual Layer break, some are unusable, some are usable/red as 4,7GB). Some believe Verbatim was the best, which I do not say, because I did not test it. I use a work around, because I had one Platinum DVD+R DL (cheap brand) stopping at 4,7GB. The work arround is, to start the Mac new before every burning of a DVD+R DL. (I mean for every single disk).
If there is a drive in it, that can't read +R DL, maybe you will be lucky getting a cheap DVD+R DL Drive on Ebay (in Germany you get them for 5-8EUR including shipping).
Edit: ...and on the legal thing - I agree it is always useful to have an image or copy of the original media, if your own gets useless.