Consider Onset Hobo Oxygen data logger, ~$1000 or oxygen probe.  Oxygen in groundwater typically low.  One of those suction pumps that uses flexible tubing might be able to pull up water if not too deep, run until oxygen removed in sample container, and quick chemistry and titration may limit change in oxygen.  For research purpose, probe or data logger best probably, and unless well is open, access for sampling or monitoring may be limited.  

The simplest way is to use an indicator dye like methylene blue which will indicate the status of oxygenation.

The pump I was thinking about is a peristaltic pump, and I think it might limit oxygen contact and exposure after it has been operating for a while.  I am not sure on its vertical limit on pulling up samples in a well.  There are several companies that make these and information on the internet.  I suppose you could use this pump to pull water into your glove box, I dont know.  I never went to that extreme, and in streams, we filled the bottle under water, pulled it up, put in the reagents in the special bottle sometimes called a BOD bottle, shook it up as directed and then titrated drops for concentration.  It has been quite a while, and if you have alot to do, the probe or oxygen data logger that is submerged into the well makes sense to me.  If you need to limit oxygen transfer from the well into the well water, you might try adding olive oil or vegetable oil as it floats and would be a barrier.  Depending on what you want, you may want to pump or purge well if you want the freshest water, and if you note olive or vegetable oil coming in, you have it well purged to close to depth of pump, and going further is going to be beyond well pump level capacity.  With a submersible pump, I am not sure if it draws any oxygen in its operation, but you might try that first or check with someone knowledgeable about how they work.  The submersible pump is going to deliver alot of water, the peristaltic pump is manageable on the rate of pumping, and some have variable speed motors.

Hi Alice, we commonly use a flow cell that our YSI DO (+ other parameters pH EC Temp etc) fits into and use peristaltic pump setup as William suggests to pump out of well and to directly flow through cell without contact with atmosphere, here is one we use:

https://www.ysi.com/accessory/id-005083/5083-flow-cell

Regards

Luke

Many thanks to everyone, now I have a clearer idea of the matter.

I think I will be using something like the cell Luke has linked, with a DO probe.

Does anyone know which kind of probe (optical, polarographic, pulsed polarographic or galvanic) is the most precise in the concentration range around 0?

Thank you all again!