I would advise against using a SSD for this purpose.
Although you can and if you do you should definitely use a secondary back up with either HDD or better yet a Tape drive.
SSDs used to have a longevity problem but that has been overcome, although once it eventually and inevitably fails its very difficult/impossible to do a full recovery unlike HDDs.
This isnt a problem for most users but in a professional environment tape is the standard for backups and SSDs are NEVER used as a sole source of storage in IT.
The reasons for SSDs are usually only for high performance machines, such as gaming and graphics design or servers with high disk load which all require fast CPUs to go with it or else disk speed is never the issue.
You might also be interested in data encryption, I know doctors use hand writing for this on paper and the digital equivilant would be a program called TrueCrypt which you might be interested in, its free and practically full proof.