Well, I'd get ahold of a 2.5" hard drive, and put it inside, before I tried anything else.
You don't want to be spending too much money on it.
Having said that, I'd look for a 250gb 2.5" SATA SSD, which should come in around $40.
An old MacBook can't do internet recovery.
So you're going to have to get the OS installed by either an install DVD or perhaps by a bootable USB flash drive.
Do you have access to another Mac?
If so, please tell us about it.
What OS is it running?
You can get an old version of "Lion diskmaker" here:
This MIGHT be able to create the USB flash drive installer, BUT... I don't know if this will run on a newer Mac running late-model versions of the OS.
I suggest you try it and see.
You can also BUY a Lion install DVD if Apple still sells it:
(this is the only URL I could find)
Tirez pleinement parti de votre Mac, installez Microsoft Office et Windows. Commandez en ligne avec livraison gratuite et rapide.
www.apple.com
Another thing:
If you have some way to connect the SSD to a different Mac such as:
- USB3 enclosure
- USB3/SATA dock
- USB3/SATA adapter dongle
... then you could mount the drive (alone) on your other working Mac, and see if you format it (I'd try Mac OS extended with journaling enabled) there.
But you'll need to install it into the old MacBook to run the installer.