Does anyone have any experience or opinions about using low-cost 3d printers for making adapters, mounts, etc. for a physics lab (my lab is does optics)? e.g. which materials are the best, stereolithography vs extrusion, brands, etc.
On low cost, FDM (or FFF as some call it) is the most “evolved” tech right now. stereolithography shows interesting results, but it’s much newer and less information and details are known about it. Right now, I think an extrusion printer is a safer bet. As you want to print, not toy with printers.
As for printing quality. I work for Ultimaker, so yeah, I would say: An Ultimaker is the best extrusion printer you can get quality wise. (But you don’t have to trust me on this, surely some user will drop by to confirm this 
or check the make-magazine test on 3D printers. They mark the Ultimaker as best in quality )
As for extrusion prints. There are prints in PLA and ABS. I’m personally used to seeing better prints in PLA. But PLA is not an option if it needs to absorb large shocks, or higher temperatures then 50C. ABS is harder to print, but a bit more flexible and thus more shock tolerant.
Note that printing optics (like lenses) with extrusion printers is impossible, even ‘clear’ materials will end up cloudy and with air pockets and stuff. (stereolithography might be able to do this, but I have no experience with that)
With any type of printer you will have to learn a few things. For example, plastic shrinks, dimensions of prints will be slightly off. This is no different from any production process. But people do not always expect this. If you draw a hole 3mm, it might end up being only 2.8mm due to the fabrication process. Depending on what you need, this could mean you need to go trough a few iterations of your design before it will work.
I would go for a DLP printer for optics applications. They’re more precise but weaker.
Define low cost.
FDM: lowest cost machine and material, wide variety of material adapted to funcional parts, low detail
SLA: the opposite
Also I am assuming that you are looking to make carriages, not lenses, If you are making lenses there is not a printer that will work in your Low cost definition. The optical quality of SL is not high enough. If you are looking for simple mounts, slides, and other structures FDM or FFF would be fine.
You really need to define Low Cost. Some people consider $500 low cost, others consider $5,000. If you can actually pin down low cost then you can start to get recommendations.
Thanks everyone for the advice. I would not be printing optics, just mounts, spacers, and adapters to hold lenses and mirrors.
Rigidity is probably the main quality I would look for in a material, followed by resolution (i.e. detail size). Shock resistance is not a requirement.
My price limit would be 5000 USD. Ease of use and reliability are also of high value. I don’t want to fiddle with it too much.
Right now, we make parts out of aluminum or plastic in a machine shop with mills, drills, lathes, and saws. I am looking to simplify the production of these one-off parts.
If you send me an stl of a smaller piece I can print it for you in abs or pla as a demo. I plan to start using polycarbonate in the future as well. Just pay shipping? I agree with @Daid_Braam , ultimakers are quite nice, and you can get them already assembled. Personally I went with a mendel90 for the lower price and comparable quality.