I would recommend replacing the HD with a SSHD hybrid drive as the better direction. You need this older series Seagate laptop SSHD drive. The newer FireCuda series does not support older SATA port systems.
While an SSD could be used, the OS (OS-X 10.7.x Lion) used on the older MacBooks does not offer TRIM support and you'll need an auto SATA port sensing drive like Samsung 750 EVO SSD
If you review the two spec sheets you'll see both offer support for SATA I (1.5 Gb/s). What ever drive you go with will need to support this SATA speed. You can't use either a fixed SATA II (3.0 gb/s) or SATA III (6.0 gb/s) drive as they are too fast for your system.
As for using an optical drive carrier to support a second drive be aware the PATA port this system has doesn't offer much speed (much slower that the SATA port) so it would not make sense to put a SSD drive in it and the other problem here is the optical drive port does not offer crash guard protection so if you put your HD in it a good bang while its running will ruin it. Double dammed!
Last point here is think through the costs and remember Apple no longer offers OS support and many apps today won't run on this older OS.