Sybase produce a number of database products under the "Adaptive Server" brand.
Adaptive Server Anywhere:
Small footprint typically deployed on Windows NT, but can also be deployed on a number of Unix platforms (Solaris, Linux, HPUX). This is also known as "ASA". Each ASA manages a single database. It supports Transact SQL - up to a point, triggers are very different and is almost completely self managing.
Adaptive Server Enterprise:
This is probably what you're looking for. It was previously known as Sybase SQL Server, but after Microsoft bought the code line to SQL Server 4.2 (or whatever) Sybase renamed the product to differentiate between the two. In the industry "SQL Server" generally refers to the MS product.
Adaptive Server IQ:
This is an optimised product for large read only or low transaction rate databases. The product heavily indexes the data in such a way updates can be quite slow compared to a normal RDBMS. This product works well above 25GB.
Getting access to training material is a little difficult short of going on the courses. There are a number of books but nowhere nearly as many for MS SQL Server or Oracle. If your looking to learn Transact SQL, O'reilly produce two books on the subject. I suppose it's quite possible to pick up a book aimed at MS SQL server and use that as well for the programming side of things. Have a look at http://www.amazon.com
ASE Admin is quite different from MS SQL server, particularly on Unix and with versions of ASE less than 12.0 I suggest also being familar with the OS you're going to run the server on. The Windows NT version of ASE will NOT run on Win 95, 98, ME etc.
The developer licence includes all the licenceable options (Full text search, java etc). The licence states that it can only be used on a single CPU and is limited to 25 connections. Which sounds ideal as a learning platform.