I too make my own MP. Not with SLS or other powdered/prilled surfactant.
I don't have any problems with SLS. It is a perfect cleaner; not too mild but, as long as you compensate with Cocomide Betain in your recipe for example, which make the SLS milder, you're good. (You seldom use only one surfactant in a product anyway.)
Some ingredients have a bad name - mostly hear-say or misinterpretation. Just like they say that a lot of coconut oil in a soap would dry out your skin.
Some people are more sensitive than others. For those customers I make products that contain different and milder surfactants.
I like SCI (Sodium Cocoyl Isethionate) a lot!
Have a look
here to learn more about surfactants. Susan's blog is fabulous!
And she is a surfactant guru.
eta: totally ignored your question - shame on me!
I think any base is good. There is a tendency to leave SLS out of the industrial MP; here (EU) it is hardly available anymore; perhaps still in craftstores.