BJT - DC Negative Feedback Biasing
Ic is dependant on Vbe and is always near 600 mV at Ic =1.00 mA but varies  beyond this due to rBE losses dependent on size of chip.
So if you choose Vbe to be 600mV , linearize it with a small Re =50 Ohms or 50mV and design CC for 1.0 mA.
Then Vb=650mV for Ic=1mA and Vc depends on load.  Still there is contention between current source and current sink, so you were right to add negative feedback, but now you need to add voltage feedback to base with a series Rin to regulate voltage with Rin/(Rin+Rfb) to balance the voltage between Vin and Vc to achieve Vb=650mV.
can you do this? While making Ifb &lt;&lt;1mA
Otherwise without Re ,   Add a series R to base and then... Vc=(Vin-600mV)/Rs depends on hFE which you cannot control as easily as there is a ≈50% tolerance on hFE.
Round down all numbers to 2 sig figs.
falstad’s website has an excellent electrical simulator. look for my examples.
However for an AC coupled load your voltage gain is dropped significantly due higher source impedance but then Zout is reduced by the voltage feedback gain. Which is a separate issue. Expect about half of Rfb/Rin ratio since hFE is much lower than an Op Amp and Rfb output impedance is reduced by the gain thru that R.