OP wrote:
"Should I transfer the OS to the new SSD or something like that? "
IF you believe that your current OS installation is "in good shape", you could do this:
1. Buy the USB3/SATA adapter dongle I mentioned in reply 4 above
2. Download CarbonCopyCloner (FREE to download and use for 30 days, this will cost you nothing)
3. Connect the SSD to the Macbook using the adapter
4. Open Disk Utility and erase it to Mac OS extended with journaling enabled
5. Run DU's "repair disk" function on the newly-formatted drive, just to check it before using
6. Open CCC. Put your source drive (internal) on the left. Put the target (SSD) to the right
7. Accept CCC's defaults and turn it loose.
8. If CCC wants to clone over the recovery partition, YES, you want to do this too.
9. When done, quit CCC and power down ALL THE WAY OFF
10. Now, do a TEST BOOT: Press the power on button and IMMEDIATELY hold down the option key and KEEP HOLDING IT DOWN until the startup manager appears.
11. You should see the icon for the external SSD in startup manager. Click it with the pointer and hit return
12. Now, the moment of truth: do you get "a good boot"?
13. If you do, check "about this Mac" to be sure you're booted from the external. It will look EXACTLY like the internal "looked" (because it's a clone, right?)
14. Take "a look around" at things. If everything is OK, power down.
15. NOW is the time to get out the tools and do the "drive swap".
16. After you close up and are ready to try the SSD "inside", you need to AGAIN boot with the "option key trick" I mentioned above.
17. When you get to the finder, open the "startup disk" preference pane and re-designate the SSD to be the new boot drive.
18. This should do it.
PRINT THIS REPLY OUT and save it.
Check it off as you go along, and I guarantee a 98% chance of success.
I'm that confident.