I believe database Domains will accomplish what you're looking for.
From Catalog, right click your gdb and select Properties, then go to the Domain tab.
Start typing in the Domain name box to create a domain.
Below, Select the field type you want to apply the domain to. This is the type of values you want stored in the database.
In the next box down, type all the values you want stored in the database in the Code column. The description column will be what users see in the interface. So if your code was 1, and the Description was "Open", users would see the choice "Open", but the value 1 would be stored in the database.
To apply the domain, open arc toolbox, go to Data Management > Domains > Assign Domain to Field
and choose the field you want to limit data entry on.
Once that is complete, users editing the field will be presented with a dropdown list of the values specified in the code/value pairs of the domain.