You might want to read construction tips from the FM side before you begin; these are tricks I have learned over time and will be helpful in the construction of any radio so it doesn't feed back on itself and oscillate.
This radio may need a little tweaking because of component
tolorences, but it performed better than the one in my clock radio,
feel free to copy the schematic.
If you want to see how well it works minus computer RFI here.