Best source for and kilo-ohm value to use to replace 2 turntable speed control pots?

Just last week I ran into the same problem with volume pot for Philips, bought substitute from DigiKey. You must know max resistance for the pots and choose the ones which have appropriate dimensions. They wont look exactly the same, but with some luck you find something which can be fitted without too much drilling

I don't know what turntable that is (Ariston???), and just to know where the pots are located tells us nothing about what pots you need.  You need to acquire a schematic or a parts list for your particular turntable.  From either of those sources, you likely can determine what value potentiometer was originally used.  Then, replace like with like.  There are log taper and linear taper potentiometers available for most any particular value.  Getting a part number would be ideal.  Removing the two pots from the chassis and examining them for any labels might also do the trick.  Some pots are stamped with their value and other info.