A switch just basically adds more lan ports to your router it is a very stupid device. The router is what makes the internet work. It receives the ip address from your ISP and shares it between your machines.
You can not bypass the router function....well you can but then you can only run 1 machine on your connection.
Many things can be causing drops most likely some issue with the internet connection itself rather than a issue with the router. Even very inexpensive routers can keep up with most internet connections. If your connection is over say 300mbps then you need a more powerful router but in general a router that is under powered will not drop your connection it will just not run the maximum speed you pay for.