Several years ago Nuts and Volts Magazine had the schematic and construction details for a gizmo called the Decade Pot Box. Basically it uses potentiometers in values of 10; i.e., 1 Meg, 100K, 10K, 1K, and 100 Ohm, and a five position rotary switch to select between them.
The theory is that you connect the box to your circuit with jumper leads and turn the appropriate pot until you get what you want, then measure with an Ohmmeter to see what the value is so you can select your fixed resistor.
The thing is, there usually aren’t that many different resistor values you need to use. Especially if you make it a habit (a good one) of using the same parts over and over - every white variety LED I’ve seen, a 1K resistor is what you want. If you use bulbs for certain effects, use the same ones - all bulbs with the same ratign will use the same value resistor, no need to stock dozens.
Also - why are you using your meter to get the value for your resistors? They have color codes on them for that.
Black = 0
Brown = 1
Red = 2
Orange = 3
Yellow = 4
Green = 5
Blue = 6
Violet = 7
Gray = 8
White = 9
For the first 2 bands. For the third band, it’s the number of 0’s to add to the end - whatever number is how many zeroes, ie if green it’s 5 zeroes. Fourth band if there is one is silver or gold for tolerance, sometimes others for precision resistors. Gold = 5%, silver = 10%. So a brown-black-red would be 1, 0, and 2 more zeroes, 1000 = 1K. Yellow Violet Orange would be 4, 7, 3 zeroes = 47000 = 47K.
I think one or more potentiometers would do nicely. What range of resistors would you expect to use? How about a 500 Ohm, a 1K (1000) Ohm, and maybe a 2K or 5K. When you hook one in, you need to be careful that you start at the max setting instead of the min - which is zero Ohms and will blow out your accessory. Start with the largest potentiometer first and work your way down. You might want to install a series fixed-resistor so you can’t accidentally reduce the resistance too low - for example put a 100 Ohm resistor in series with the 500 Ohm pot. Then you’ll get 100-600 instead of 0-500.