Broadcom/realtek Driver update?

Broadcom 4313 802.11b/g/n I have not tried to update the driver until someone tells me it's the right thing to do. I'm not wanting to make more trouble, I just want to get my two laptops to connect without this hit and miss stuff.

My other brand new laptop has realtek PCIe GBE Family Controller also listed under network adapters yet they are the same brand of computer. Is this normal? shouldn't they be matching? It's the realtek one that is having the connecting issue the most. Neither have been updated but I want someone to tell me it's safe to update as I don't want to mess anything up.

Then configure your network connection in the bottom-right System Tray using Windows 7's built-in superior connection manager, since HP's adds 30 second to boot time and hogs CPU. Troubleshooting with MSCONFIG

What does this mean "use the built in win 7's superior connection manager?" Is the HP manager that little icon in the bottom right task manager that I click 'connect' to the internet?

If I used the windows built in one, would I have a little icon in the task bar to be able to click connect/troubleshoot, etc?

My specs for our two new laptops are below. One may get kicked offline but I can repair connection. The other one gets kicked off randomly and won't reconnect after troubleshoot.

I'm here and waiting for some help.