What are some things and techniques I can do to minimize the time it takes for my apps/updates to be approved for the App Store? Do smaller updates generally take less time, and
I cannot post a comment yet, so I am posting this as an answer to your question based on my experience submitting new apps, as well as updates to existing apps in iTunesConnect.
Unfortunately there really isn't anything you can do to speed up the process, aside from fixing the issues in your app if it gets rejected, and re-submitting asap.
Apple allows you to request an expedited app review.
https://developer.apple.com/contact/app-store/?topic=expedite
Please note: If you're facing extenuating circumstances, you can request the review of your app to be expedited by completing the form below. Expedited reviews are granted on a limited basis and we cannot guarantee that every request will be approved.
I have personally used it twice. Once for a cosmetic issue in an app, which was rejected. Another time for a critical bug fix, which was accepted. I wrote a very detailed explanation of what my application did, what the bug was, why the bug was important to our (Mine and Apple's) customer.
One thing I have found is that free apps versus paid apps sometimes take different amounts of time.
For example I have a paid and free version of the same app. I submitted an updated for both one right after the other. First I submitted the free version, then I submitted the paid version immediately after. For some reason the paid version went into review, and was approved a day later, where as the free version is still waiting for review even know I submitted it first. I suspect that free and paid apps have different 'queues' or 'priorities' over at apple.