A quick caveat, I am not based in the US and can’t guarantee my suggestion necessarily comply with those regulations.
Personally, I would definitely outsource the actual microbial challenge testing. For new developments in a small company, I would find a microbial testing kit to use during development and then get the challenge test of a seemingly microbially stable formulation completed elsewhere.
If you use an external safety assessor they are also more likely to immediately accept an approved report from an accredited lab than in-house testing (where the methodology will be looked more into).
Also, when doing challenge testing on a new product consider sending multiple samples with different preservation systems - you’ll save yourself a lot of waiting time this way if some are rejected.
What if I just wanted to do stability testing?
As for general stability testing, in general, you should get equipment for measuring your stability endpoints (these vary depending on the product but can include a viscometer, refractometer, colourimeter (particularly for colour cosmetics), microscope and ). A centrifuge for a quick and dirty stability test and an oven + freezer for accelerated and freeze-thaw stress tests.