What is the best network solution for a campus design, installing the L3 switch or (L2 switch + router) and why?

Layer 3 is good option. But if you already have a Router in your network, then add the layer 2 switch and save the money.

in fact, the solution depends on the company needs, but usually in campus network design, switch L3 is better because of fast switching and routing through the Vlans.

Installation of L3 devices always gives you better services and security. Management of such devices are easy.