Define "good"?
You get what you pay for and pots vary in price from 50p to over £50. (YES, £50 for a pot!).
For 8-bit PICAXE use, a cheap carbon pot should be just fine. Should also be OK for 10-bit with a little care.
The problem with carbon pots is that they dry out. (crackle when you turn up the volume on an old radio)
A quick spray of cheap aftershave on a crackly pot works wonders!
Carbon actually generates noise but it should not be a problem until working at > 12-bit. (hiss on a cheap radio)
If you have a lot of random variation on your reading even when not moving the pot, then as hippy says, something is wrong.
Things to look for:-
Wrong ADC connection.
Wrong value pot. (should be 10k, 20k or above will cause erroneous readings.
Long wires. These will pick up mains hum just like a HiFi does.
Proximity to a power supply. Switchmode supplies transmit a lot of noise and transformers transmit a lot of mains hum.
Filtering can help to remove unwanted noise but it is always better to avoid letting it in than it is to let it in and then remove it.
I religiously put a 0.1uF on any ADC input. No need for a resistor because the pot itself will provide sufficient source impedance.