If you're considering Desktop SQL Server for your own use, I'm not sure how much that would help with file size. You'd be using same platform.
The advantage of SQLServer on a server system, is primarily to provide many live connections to multiple databases for multiple users. Typically a server machine has more disk and is faster than PC, so a performance improvement is likely, even with only one user.
Other advantages of SQLServer is that it provides excellent security (SQL Slammer worm attack not typical problem). Also, database backup and recovery are more sophisticated. Other applications that use SQLServer can run on top of it.
It uses ANSI SQL 92 standard, Scripted jobs can be run on scheduled basis, SQLMail reports job results and alerts such a log file full, etc.
Also, transactions (updates) can be logged and used for up to the minute recovery along with a prior db backup.
If this is not what you need, I'd suggest staying with Access and adding RAM and faster disk drives and a faster processor. I don't know if multiple processors would benefit Desktop SQLServer (they sure make the Server version rip) and I doubt if Access would. The Desktop version would benefit from adding RAM because it puts part of TEMPDB database in RAM for increased query parsing and execution speed.
Hope this helps