Someone PM'd me recently about my thoughts on doing this so far, so I'll paste in what I wrote - let me know if there's anything else that would be of use!
We decided that we wanted to get a 3D printer for our ICT department - the primary school where I teach is subject taught, so I have dedicated ICT lessons with Reception up to Year 6. I wanted to make the 3D printing project cross-curricular with Art/DT and Maths into a big project, but I found it difficult to explain what I was doing to those teachers and so decided to go it alone for a term instead.
We looked around at a lot of different 3D printers and eventually chose this one:Cube 3D printer tech specs. We considered building our own - cheaper and more reliable - but got cold feet as the Headteacher was expecting results and I was terrified of messing up the building part! Cube3D sell themselves as being the most user-friendly, which they may well be but there's also quite a big lie about how simple printing is - it's not. You have to calibrate it perfectly every time or it won't work. With practice it gets easier, but it's certainly not as hassle-free as they present it to be. It is also very slow - I printed a teacup and it took 4-5 hours. Not a problem necessarily, but something to consider if you have to print 50 separate models (which I did!)
I wouldn't particularly recommend Cube3D model 2 for a few reasons, but it looks like it's already been updated to Cube3D 3 - I imagine they've ironed out a lot of the issues we had. Having said that their help team were incredibly good (once we were able to get in touch with them!). I've heard very good things about CubeX (CubeX features & specs | Cubify.com) and Makerbot (https://www.makerbot.com/) but I think these are more expensive. Also it's worth mentioning that the materials are very cheap, so no need to worry about that element.
In the end, I decided to get my Year 6s to design robots using a free CAD software I found on the internet - FREECAD (FreeCAD: An Open Source parametric 3D CAD modeler). I wouldn't recommend this! Firstly, 3D printers are still very basic and they really need to print models with a strong base or they collapse a bit - buildings, castles etc would be perfect. Robots with stick-thin legs are definitely not! Secondly, the CAD software we used was extremely glitchy - free and simple enough for primary children to use (difficult to find one that is both), but badly designed.
If I could go back and redo everything again, I would get the children to build something like a castle using this program I later found - Autodesk 123D Design. Brilliant and simple, with lots of templates that children can easily adapt themselves. If each child could get an email account to run it off it would be even better!
I think that's all I can remember about it. Feel free to ask away though - I know how little there is out there about this as a teaching topic!