I got an 2.8l 89 firebird with only 80K miles...just bough it like a month ago...but I got a problem...

Its kind of hard to start it:

The guy I bough it from said It had not been started in about 2 months

-the engine rotates but takes a while to start...usually about 3 tries and holding each one for about 3-5 seconds...pumping the gas seems to help a little...Also when car is running and I turn it off...IT STARTS RIGHT UP everytime (I assume engine is still hot)...but after a couple hours or so of cooling off...It takes a while to start again
when started...engine sounds good...but there is a clicking noise that seems to be to be coming from the manifold or gasket area ...and tranny shifts fine...but when I start going and press the accelerator the noise gets louder

I have yet to do a tune up on it...which I hope will fix problem ...spark plugs...my friend told me my timing was probably off or a bad gasket in the manifold/headers

 

I'd do the tune up first and then see what other bugs need to be worked out. could just be a rocker arm needing some adjustment. As for the starting hesitation, could be fuel or spark.

 

The F-body V6 engines are known for cracked exhaust manifolds. That is probably what is causing the noise.

For the hard to start problem I would hook up a pressure gauge to the shrader valve on the fuel rail and see how long its holding fuel pressure after the engine/fuel pump is turned off.

 

Had this problem with my TPI. System came off 89 Formula, but I got a computer from an 88. Added a cold start injector and now it starts up fine everytime. Your cold start injector may be clogged or failed. Or it could be the switch at the front of the intake for the cold start. My suggestion is to look at this first. As for the noise, sounds just like what Dens71TA had said.