What kind of router do I need for routing between two subnets?

If your biggest problem is the lack of availability of IP addresses, then perhaps the easiest solution is simply to use a Class B address behind the router rather than a Class C.

If your network is configured as 10.10.0.0 (subnet 255.255.0.0) you would then have 255 X 255 available IP addresses (65,000 + IPs available).

Your router address would become 10.10.0.1, and similar adjustments would be made to DHCP, etc.  This requires no new hardware and provides more than enough IP addresses for your Internal network -- if that's what the problem is.

On the other hand, if you are attempting to isolate or segment various groups for security purposes, this won't do it.

Thank you guys.
 
We have a Cisco 1841 router for us to connect to internet but it is property of our ISP and we have no access to it. Other than that we don't have any other router. The Cisco 1841 router connects to an ASA 5510 and then two HP V1810-48G switches.

Expanding to a bigger network with more hosts is not an option due to potential broadcast storm.

As mentioned we currently have only one subnet 10.10.10.0/24 . We want to add one more subnet 10.10.20.0/24 and look for a router for routing. As your recommendation, the answer boiled down to either a L3 switch (Cisco small business 300) or a router (Cisco 2600). Can you give pros and cons of using a L3 swithc/a router in our case mentined above?

Thanks.

We ended up using one of the physical ports at the Cisco ASA 5510 to create a VLAN for that specific subnet, and as the result it doesn't need any router or L3 switch. Thanks for you guys's help.