Actually the usual method of interacting with Access databases is SQL.. the default storage mechanism is JET, which uses SQL, but isn't especially compliant to the interantional standard (but what SQL engine is truly compliant). Access can talk to other data storage mechanisms such as server SQL's: MySQL, SQL Server DB2 etc...
However Access does a good job hiding a lot of the SQL for you, or doing it in background. Its not really a problem, all of the queries SQL can be seen, even now in a few shameful moments I still fire up the Access query browser just to make sure I'm on the right track. The SQL you virtually never see in Access is DDL.. creating or modifying tables.. but you can write that style of SQL if you wish or have to
What it comes down to in my view is what to want to achieve.
If its for a specific project then understanding some of the SQL concepts then virtually any db will do. The problem I can see there is that to create a meaningful data model and get some data in could be tricky for a first project.
If you want to 'mess around' and create a few learning applications interfacing with SQL then unless you have something like a web server (in which case PHP/MYSQL or ASP/MS SQL Server would be natural choices) or a development language such as
VB, C (And all its children), Delphi etc then there are precious few routes to get something to store data that is straightforward enough to manipulate unless you go down the Access route.
So If I were you I'd approach it two ways sure use a server SQL if you wish.... if this is for CV tilillation I'd download the SQL server developer edition (free) as employers do like the look of that.
If I were you I'd want to look at the dreaded Northwind db that used to (don't know if it still does) come with Access and SQL server.. if you cna get both even better then you can see soem of the differences between the SQL server version and the Access/JET version. The reason being its a fairly well documented db, it has some meaningful data and its already available.
enjoy