hmm maybe a microscope, few slides, stains, petri dishes some culture medium you can probably whip it up at home. Ignoring the cost of the microscope you can probably do this under 50 dollars maybe even less

If you don’t have the ability to do staining and culturing, it would be really hard to test acne the way you are thinking.

When you culture bacteria from skin, you have to use several, let’s call them dichotomous keys, to determine what kind of bacteria you are looking at. Gram stain is the first step, but then cell shape, cluster patterns, etc all indicate what kind it is. This is important because you probably want to only culture Propionibacterium acnes (if I remember right, this is the bacteria implicated in acne formation). However, there is more Staphylococcus epidermidis on your skin than P. acnes.

I suggest you find 10 volunteers who have acne. Five experimental and five control. Use placebo on the control group. Have them volunteer to not use their normal acne medication for the duration of the experiment.

Make sure you count the acne on each person on day one. Then wait a week without any acne treatment. Give them all a generic face-gentle soap to keep clean with. And then recount. After that, start applying your herbal remedy to one group. If the remedy requires a solution of some sort, make sure you use the exact same ingredients (minus the herbs) on the placebo.

Finally, to make this really a publishable type of experiment, you need to ask someone who does not know who is control and who is experimental to do all of the observing, counting, recording for you. This keeps you from making biased measurements. At this point, the experiment is considered a double blind, placebo controlled study. Double blind because neither the person assessing nor the person being assessed know whether or not they are the test group or the experimental group.
Make sure, at the end of the test, to have each volunteer answer some basic questions, such as, how often did you wash your face every day, etc. The questions need to deal with the uncontrollable variables to give you an indication of what other experiments could support your conclusions.