Been quite happy with PCBWay, with batch sizes between 30 and 130. Fast and surprisingly clear communication. Some mistakes do happen, but it's not surprising with relatively complex designs. They'll source everything, or in one case, I have supplied them with one BOM item, while they sourced the rest. I haven't spotted any fake parts, but not saying it couldn't happen.
Having heard and seen horror stories of modern Western PCBA quality, I'm not complaining. Completely error-free PCBA is not going to happen without a huge investment on your part. PCBWay has been quite hassle-free and low-cost, even in small batches. But you will need to perform your own quality control and possibly some minor rework, which they will compensate for if you complain. If a major error happens, any PCBA house should fix their error by redoing the boards. Haven't happened to me, yet...
It sounds like your designs would be smaller than mine. So expect around $200-300 initial cost (possibly even less, I don't know) and off you go. But beware - you need to buy excess components for the pick&place because some parts will always be lost in the process (for very small scale, they'll hand place everything, but excess parts are still needed). In very small scale, this can easily lead to 10-20% of extra BOM cost. This is true with any assembly house. If you buy the sourcing service, expect to see a bit of extra price played into the component prices. This is a combination of taxes and tariffs, pick/place excess, and their business model of hiding part of the cost to the component prices, which is kind of understandable - sourcing takes resources as well.