I've done a bunch of builds like that before.
Typically, machine shops specialize in some form of manufacturing type (milling / lathing metal, for example) or specific niche (metal stamping). If your parts require different manufacturing processes, you may potentially need multiple shops to get that done.
I found that Chinese machine shops are going to be both cheaper (about 8x in my experience) and faster lead time than North American shops. The exception will be that if you need something highly specialized (e.g. super tight tolerances), you may find it easier to get it done locally. I'll assume you'll be going with a Chinese place below. For finding Chinese places, I use Alibaba with MOQ set to 1.
Machine shops are always trying to expand and get bigger contracts with bigger customers. They dislike low order quantities and low volumes, and I found that I need to continuously cycle machine shops every couple of years as they move to larger customers. The other thing is that with manufacturing, there's a setup cost (flat cost per batch) plus a per-part cost. At single and low double-digit volumes, setup cost is going to be a lot. Make your part easy to manufacture - easy to clamp, made from readily available stock, use more readily available machining (e.g. 3 axis and not 5 axis, straight lines doable with a manual mill vs CNC), reduce manufacturing steps.
I found that cheaper machine shops (say, 2x cheaper than others) will tend to have a lower ability to understand what I'm trying to get done (will take a lot more & simpler communication) as well as a higher probability of the part being out of spec.
The more proficient you are at knowing what you want (obsessively defined specs and tolerances on everything you can think of) will get you much cheaper results. The less you spec out, the more they need to think about your design and your needs, and that's quite expensive from their side. My process is to have a drawing PDF that I send to 10 manufacturers for quotes, get 5 quotes back and select from those.