Do I have to use Rails to use a database?

Ruby has to my knowledge, 3 primary ways of using a Database.
Rails is famous for using ActiveRecord, but ActiveRecord can be used
independently of Rails. Its well worth learning as it makes database
use very easy indeed.

Another Ruby framework Nitro uses a database layer called Og (ObjectGraph)
which I presume (not sure) can be used externally to Nitro.

Lastly theres the default, DBI. This is a more conventional database access
library, where you are kept pretty close to the SQL mechanisms.

I'd say using rails is a bit of overkill, and you seem to have come
to this conclusion as well. i'd also go so far as to say that using
activerecord would be overkill for something simple like your menu.
you most likely would never use the things that make activerecord
beneficial.

if you want something more lightweight than activerecord, check out
DBI, which was suggested previously. as far as the actual database
goes, you might want to take a look at sqlite3 as opposed to something
like mysql/postgresql/etc.

dbi:

http://ruby-dbi.rubyforge.org/

sqlite3:

http://www.sqlite.org/

download for ruby-dbi is:

http://rubyforge.org/projects/ruby-dbi/

see the first link i sent, that has the installation instructions for ruby-dbi

http://ruby-dbi.rubyforge.org/

if you are on shared hosting, then your provider may already have dbi
installed. you'd have to talk to them to know for sure (or write a
test script).