A series output cap of about -j62 ohms and a shunt parallel coil at output of device of +j56.5 ohms will match to 50 ohms real. Make the coil a little lower in inductance to be able to resonate out any additional stray capacitance.
Just about any RF amp is going to have an interaction between input and output loadings due to S12 feedback. Optimum input match for maximum power gain may be different then match for best noise figure.
Depending on frequency, type of device, and other requirements like dynamic range, different techniques can be employed. If you have some excess gain you can tolerate to reduce, one of the best things you can do to improve stability is to put some shunt resistance across output parallel coil. This will help overall stability and stabilize output match somewhat with little effect on input noise figure.