Welcome to Chordie, Newbie.
I'm only guessing, but the strings probably aren't the problem. There are a couple things that may be causing the "humming" or "buzzing". First, you may be touching extra strings with your fingers. A narrower neck may actually make this problem worse since the strings are closer together. It will just take practice to get it right. Keep in mind that you need to push straight down with your fingertips. If you have short fingers, it may be more difficult to come straight in on the string (again, practice). I think this may be your problem since you mentioned it got worse when you played chords.
Another thing you could do is make sure that you are playing as close to the frets as possible. This will help ensure that your string make contact with the fret and it will play the right note without humming. Once you develop more hand strength that won't be as crucial but it's definitely a good habit to get into. Again, practice, practice, practice. You've only been at it for six weeks, you'll get the hang of it after awhile.
You could try new strings as well. I would suggest going with light or extra light gauge (lighter gauge strings don't sound as good, but they are easier to play). I think you may be talking about Elixer strings which are expensive but good. They're what I use (polywebs). But keep in mind that if you change the gauge of your strings, you will change the action of your guitar (how far the strings are from the fingerboard). Take it into a shop and figure out what gauge strings are on it and if you're going to change the gauge, have the tech change the strings for you and set it up for you at the same time.
I know this was a long answer but I hope this helps.