What makes a good fighter? Depends. I presume you're referring to nowadays? The Spitfire was the greatest fighter in existence in it's day, but I don't see many nations lining up for it now...
IMHO, the basics for a great fighter include: excellent thrust to weight ratio, large payload capacity, advanced avionics, good RCS, good range performance, an "unstable" aircraft design, good EWSP and advanced weapon systems.
Any fighter however is a compromise between design issues. Each has relative strengths and weaknesses. Fighters such as F-16, F-18 series, Mirage 2000 and MiG-29 are all good highly maneuverable aircraft that can carry reasonable payloads. They are reasonably priced, but have several important limitations.
They are range limited. If you try and increase their range with external fuel tanks, conformal fuel tanks etc, you reduce the aircraft's agility and the payload it can carry.
Aircraft such as F-15, F-22, SU-30 are big aircraft with excellent performance, excellent range and payload capabilities. They are also expensive to acquire and expensive to operate.
It's all a matter of National defence requirements, strategic and political reality and doctrinal and financial issues. There is no fighter that is perfect for every situation and Country...
The best air to air fighter in existence is arguably the F-15 series of fighters. 101 A2A victories and no losses in over 20 years of service is pretty hard to go past...