I'm unclear what you mean by "work properly with". I think you're going to be disappointed with the results because of the age of the 2514 router, but I'll give you the technical details and let you decide. I think the router is going to be the biggest disappointment, and using a 2500-series Ethernet switch isn't going to make the router any prettier.
A 2514 router has two Ethernet ports. The Catalyst 3500 series devices are Ethernet switches. You will be able to connect the devices to each other and the 2514 router will be able to route packets (protocols supported will depend on the specific IOS version installed on the router) received from the switches via Ethernet.
That's not to say it'll be easy to connect the two.
A 2514 has dual 10Base Ethernet connections on AUI (DB-15) ports. You'll have to use an AUI transceiver to connect it to any modern 10/100 Ethernet switch via UTP cabling. You'll be limited to 10Mb/sec bandwidth between the switch and the router, which rules out using the router for any kind of "router on a stick" application for inter-VLAN routing.
Finally, from a software perspective you'll probably be disappointed in the IOS versions you can run and the capabilities of the router, given its age.
If you're talking about using this router to route, say, a T1-based Internet or WAN connection I think you'd be better off spending a little more money and getting a more modern used router (a 2600 series, for example) and not having to deal with the AUI ports.