As John is stating, you need a router to be able to pass information between two different networks. Technically a basic layer 2 switch doesn't care what network range something is in, it's all running off of MAC addresses. However, your computer network operates at layer 3, and thus even if you directly connect the switches together, you will not be able to properly direct traffic from one network range to the other. You need a router for this.
Determining what router you should use is going to be pretty complex though. It comes down to a lot of factors including what amount of traffic bandwidth and bandwidth management features your business needs, what type of quality of service or similar features you might need, and security features. For instance, what do you already have in place that actually connects to your switches and allows devices out onto the internet?
If you don't have anything yet, then I'd recommend taking a look into at least an entry-level business firewall. Most all of these units can give you a lot of network customization such as multiple network ranges and quality of service, but also give you security features that might not be found on something like a layer 3 switch or basic router. I have had great luck with the Sonicwall TZ series firewalls, but again picking the exactly right one for your needs is going to be determined based on a lot of other factors including network size, necessary security features or VPN features, etc.
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