BASIC is a good place to start. Hense the name

It lets you learn programming concepts (input/output, variables, if-then, loops, etc) without exposing all the exotic stuff. Once you learn the concepts, they apply to all other languages; the syntax might change but the ideas are the same.
I believe C++ is widely used for games, only because it gives you lots of control over memory and speed. I haven't heard of BLITZ, but I never got into the game stuff

.. My programming experience has been mainly business applications and websites. You don't see C++ in too many business applications, because they usually focus on "RAD" (rapid application development) which typically involves VB.Net, Java, etc (these languages provide functions for a lot of the nitty gritty stuff that you have to do yourself in C++; e.g. array searches, string manipulation, etc)
I think it's important to know programming concepts, even if you're not planning to become a programmer. If you're troubleshooting systems or applications, it helps to understand how programs work so that you can understand what is going on. I've never been a full-time programmer, it's always just been a hobby for me, but it's helped a lot during my career.
I started learning BASIC on a Commodore 64 when I was about 10 years old (making simple tet based games). After that I gota copy of QuickBasic for DOS and played with that until highschool when I got a copy of TurboC (making ANSI viewers and "zines" and stuff during the BBS era). Next I learned PHP and MySQL (creating some websites for friends, and small applications at an ISP I worked for.) The MySQL experience got me into learning Microsoft SQL. A few years later while working for an IT company we started selling a Point-of-Sale software (cash register, inventory, etc) that used MSSQL and allows you to program add-ins via COM. This is when I picked up VB.Net and taught myself OOP concepts (object oriented programming; which was a world of a difference from anything I had done before.)
My job today is mainly systems analysis and management for a mid-sized maufacturer (I take care of their ERP software, Mail server, network routers, Windows servers, etc). However I wind up doing a fair bit of programming when it comes to creating reports, using MSSQL (programming T-SQL functions and SQL Views) and Crystal Reports (field formulas). I've also been working on a few data collection appliations using VB.Net and ASP.Net. Programming knowledge has definately helped, even thought I'm not a "programmer" per se.