Hello,
To get both VLANs on both switches your best bet would probably be a trunk link carrying all the VLANs between the two switches.
Simply create the same VLANs on the new SG300, and then configure the port that will be connecting to the 200 as a trunk port, with the correct VLANs added. Each trunk link has one untagged VLAN and the rest are tagged. Set the port on the 200 the same way, Trunk with the tagged and untagged VLANs matching. Then just plug them up and assign ports to the correct VLAN as needed.
As for if you need fiber that sort of depends. You can setup a trunk link with regular ethernet just the same, so it mostly comes down to how far apart these two switches will be. Ethernet will only reach about 90 meters, so if they are farther then that fiber is really your only option. However if they are just going to be right next to each other, then go ahead and just use Ethernet, the result will be the same.
If you do need any assistance getting those trunk links configured don't hesitate to give us a call at the SBSC and we can help get that setup.
Cisco Small Business Support Center Contact Numbers
Hope that helps,
Christopher Ebert - Advanced Network Support Engineer
Cisco Small Business Support Center
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