Rinse them well with hot water shake and flush good(4-5 X) after drinking.When I have enough stacked up over the week I use a bottle brush/baking soda hot water to clean,then drip dry,store covered,then sanitize when I use them again. You can sanitize before storing if it makes you feel better,I havent and have never had a problem because there is nothing for bacteria to grown on basically.Flushing them good < a day after drinking(preferrably after pouring them,or the end of night) is key to cleaning/sanitizing an almost already clean anyway bottle. Pre(rinsing/flushing)- cleaning makes cleaning better. Its kinda how I like to do dishes(when I do them),prerinsing.Makes cleaning way easier. No cake on crusty stuff/mold.
A jet bottle washer is not a bad idea also. I do small batches also so its not a big deal doing 16 bottles compared to 50 I guess. Although now I just recycle my own homebrew bottles when I have them,which is random so I only have to clean less than a dozen a week. Still, I think if you preflush well then when your ready to throw them in the diswasher they would be fine,although I dont think you want to use the washing detergent.
What I do and suggest is running a rinse cycle with no soap before putting your bottles in, to clear any residue. Then put your bottles in run one cycle of rinse no soap. Then run 3 cycles of dry (some have plate warmer setting) to sanitize.
this is all assuming you rinse your bottles well after each use
I use dishwasher every time. Just make sure when you take them out that there isn't any yeast still clinging to the bottom. Happens every once in a while, though I think the steam of the dry cycle sterilizes the bottles anyways.