Howdy and welcome to the Ranch.
Learning CS topics (eg programming, database, computer architecture etc) on your own is somewhat hard but not impossible.
Today's market some form of programming language (structured, OO, procedural etc) and database system (Oracle, DB2, MySQL, SQL Server) is practically a must.
From the programming point, learning data structures and algorithms will be key. Since you mentioned discrete math, this would help you to understand data structures a bit more easier I think. As for what language to start? If you look at college programming 101 course description, I bet most will use
Java, teaching object oriented (OO) concepts from day 1. But IMHO, an OO language shouldn't be the first language, but procedural. Back in the days when I was in college, my first language was C then assembly and scheme and C++. Java or PHP isn't even taught (not in the courses I took anyway). Of course C and C++ has an OO version. OO C is for iPhone dev these days.
Long story short, data structures and algorithms are key to any language. The programming language itself is really talking the programming paradigm (eg OO) rather than the actual syntax.
For DBMS, you can't get away with not knowing SQL. Is that double negative? Apart from that, learning a particular DBMS in a bit detail is good. By detail I meant able to do typical DBA tasks (eg create DB, tables, views, etc) and write functions and (SQL) stored procedures.
Which ever DB and/or programming you choose, do consider the platform or operating system it can run on. Eg Windows platform will most like use IIS as web/app server, SQL Server for DBMS and C#/VB/ASP.NET for programming.
FYR UNIX/Linux usually refer to LAMP (UNIX/Linux, Apache, MySQL, PHP/Perl/Python)
I mentioned app server along the way, which
you should get familiar with if you are doing enterprise/web development. Common (Java) app servers include Red Hat
JBoss, Oracle Glassfish, Apache
Tomcat, IBM Websphere, Oracle App Server, Oracle Weblogic, Apache Gerinomo and many more. The list can go on and on.
I should let you digest all that a bit