AVG is a (mainly) an anti virus product. It will ONLY look for viruses and thats all.
But computer security is MUCH more than just viruses, which is why companies now sell Internet Security Suites that do a whole load of things AS WELL AS looking for viruses.
Many people on here say go for AVG Free, or AVAST free and so on, but they are only anti virus products and you are much safer with a full interent security suite.
Now my guess is that Norton is a full Interent Security Suite so I would set that up and use that for its 60 days. REMOVE AVG FIRST.
As you already have already bought Kaspersky I would uninstall Norton after 60 days, and then install Kaspersky. Note the Kaspersky product will only last a year so you need to rebuy it (or something else) next year.
You should certainly only have ONE anti virus product on your PC at a time. If you have more they do indded fight with each other and it can slow your PC down.