First, the internet connection side of the network configuration is not going to matter unless you have over a 100 MB internet connection. Most ISPs do not go over a 10 to 15 MB connection for small business.
Moving to a managed switch can be a big help. I recently moved our small business from a 24 port Linksys unmanaged to a 24 port Linksys managed switch. I bought a starter Linksys SRW2024 (for about 20% of the cost of the Cisco). It has 24 1000MB ports. This switch was very easy to set up and I can learn managed switches as I go. It is not as feature packed as the bigger Cisco, but for a beginner, it is very forgiving and comes preset to learn your network.
I see a benefit from the 24 1000 MB ports for data between my engineering computeres and my server. Makes a tremendous difference. As I buy new computers (or network cards if I need the speed sooner), the other users will also start to see an improvement in internal network speed.
Hope this helps.