Internet taking ages to connect when I turn my PC on

 If it is Avast, it is probably the firewall component.  Honestly, I wouldn't even use it.  If you can install Avast internet security without the firewall component that might be a try.  Otherwise, you might just consider replacing it all together with another anti-virus like Microsoft Security Essentials.

This info. may help regarding Avast. as I use the free version now after a trial of the paid version.

Avast free version (not trial) does not have a firewall and for the features it does have (mail guard/web guard/file guard/game mode)  there is the config. option to disable any one of them.

The free version is OK (set and forget without "noise") but the firewall version should be avoided in my opinion with W7 or W8. See HERE for the different versions and features.

Should I just disable the firewall in Avast?

You can try.  I'm not familiar with Avast Internet Security.  If disabling it works, then great.  If not, there might be a way to install Avast without installing that component at all.