Blocking cell phone interference on LM386 amp
This will get a lot better once you lay out the circuit on a real PC board.  Even with a two layer board and the bottom layer being mostly a ground plane, there is a good chance the interference problem will be below the level you care about.

I wouldn't try to go for a shielded enclosure before determining it is really necessary.

Use good layout, proper bypassing caps, and small caps to ground on all signals that go off the board.  Include a chip inductor in series between the external connection and the cap on any line that can tolerate the extra few 100 m&Omega; in series.

For the caps to ground, look at capacitor datasheets carefully to make sure the capacitors have the low impedance at the RF frequency of interest that you expect.  You'll probably end up with 100 pF or so ceramic, and then choose a particular model from a particular manufacturer.  At these frequencies, there can be significant differences between 100 pF, 50 V, 0805 ceramic caps, for example, between models and manufacturer.