Starting Problems

[94sixspeedz28]

well guys im back for more help. i just recently installed many new parts on the 'Maro and i keep having more and more problems
the new parts are:
Radiator
Thermostat
Heatercore hose(had 2 make my own)
Battery
Starter
Spark Plugs(NGK Platinums)
Spark Plug Wiress
well anyway when i turn the ignition to start the car the starter sounds like its engaging for half a second and turns the motor then just keeps spinning but not turning or touching the flywheel. this is exactly what the old starter sounded like when it was going bad but how the hell could a $200 starter go bad within weeks?
also i wanted to ask you guys about pushstarting the car i do it in first but its a mission and it has to be like a 10mph roll lol(big tires are probably y) but i've heard people start in 4th cause its a smaller gear and it takes less effort.
thanks in advance