Learning mySQL is as easy as breathing. However, I would want you to start out with MSSQL. No, not because I'm a fanboi. It's just I don't have the mySQL experience and know what they offer in terms of ERD's and relational database design (which makes MSSQL a dream to work with)
Basically you need to start out understanding relational database design. A lot of people make the mistake starting out and don't learn it until they're a few projects into the thing or at a real world job. Start out early. That's why I said NO MS Access
Learn to love INNER JOIN's. Learn the difference between a LEFT OUTER JOIN etc
Does your old man want you to make the programs communicate physically with each other? Doing what exactly? (There needs to be a set purpose, making 2 programs communicate via winsock is piss easy but you don't use a spoon to cut your steak, so a little more detail would be awesome)
Winsock is a bit old-school IMO but still has its uses. If the 2 programs just need to communicate somehow with a database (display same data etc) that's easy enough too. If they
need to communicate between the two, you need to think of failover's as well.
What if one machine is down if the other one tries to communicate some valuable data?
I reckon instead of winsock's (in that case) you should look at Message Queues. (MSMQ's)
Yes Yes, I love M$ long time. But that's where my bread+butter is