Before replacing the radiator, try diagnosing some of the smaller components of the cooling system. Usually, if a radiator is bad, it will leak all at once. You may try flushing the radiator. This is pretty easy, but can be kind of time consuming. Also see if the thermostat is working. Other things that may lead to overheating is, the water pump may be shot, the fan motor may not be working, cooling fan relay, temperature sending unit. There are many reasons why it is overheating, unfortunately, most of the problems give the same symptoms.
As far as a tune up, in my opinion, it may not be a bad idea. Even though, it is fuel injected, there are still sparkplugs, plug wires, and distributor cap. ALl of these items wear out and eventually need to be replaced. It would also be a good idea to replace oil,oil filter, air filter and PCV valve. All of these things are once again,m time consuming, but not very hard at all. If you replaced the fuel filter, you should be able to do these things. Good luck. Even if these things are not the source of the problem, it will help the car to be happy any way.
The cooling issues may be a little harder to fix. Water pumps and cooling fan issues are a little harder and time consuming. I would strongly suggest going to an auto parts store and buying a service manual for the car. This will show you how to work on your exact car.