I use at least two mitts per wash, but a) only one at a time as I'm holding the mitt shut at the cuff and have the foamgun in my other hand and b) I don't differentiate between "upper and lower" section applications.
Using more than one mitt makes it easy to work quickly as I can have mitts ready and waiting in the shampoo bucket, I just toss the old one in the rinse bucket and grab another one and keep working until it's convenient to stop and agitate/etc. the ones in the rinse buckets before transferring them back to the shampoo bucket.
I do choose between different types of sheepskin (and MF) mitts depending on the job. Some are "spun", very "fuzzy" and others are more like "linger, straighter hair" in the long-nap sense. The former are softer but more likely to retain any contamination while the latter, while plenty soft enough, are a little more aggressive and rinse clean easier.
Note that I use other methods, including my BHBs, to get all the "big stuff" off, so it's not like my mitts get contaminated very often; by the time I switch from BHBs to mitts things are basically pretty clean. But if there's even a *remote* chance that a mitt is contaminated, I retire that mitt and thorougly clean it later. Most of the time, the mitts going into my rinse buckets aren't actually *soiled* and if my rinse water ends up very dirty then, given my wash regimen, it means I did something wrong.