If you go to the manufacturer's site for the motherboard it will have a list of all the supported processors, just find the fastest to maximise your systems performance.
If it is an older motherboard you may find the maximum increase in performance that you can achieve replacing the processor simply won't be worth the money.
There are a huge number of motherboards to choose from, what you need to decide first is what you are going to use the system for, if it is going to be for gaming then you will be looking for a fairly high performance mobo and CPU. You should carefully check that any new board will be compatible with your existing memory or you will also need to replace that. Likewise with the power supply. Then if you will be gaming you will also need a good graphics card.
If the PC will just be for general everyday use then you should find a package available from most good suppliers that will include a mobo, memory and CPU. Then you just need to check your power supply.
Things to watch out for. If you stick with the old power supply make sure the connectors are compatible with any new mobo. Another problem that can occur with a new mobo is the front panel connectors may need to be altered.
Any more questions, please ask. It will help if you can provide the make and model of your existing power supply and motherboard.