how much memory to buy and where do we buy it

The 2011 can also be feeling slow from a nearly full and/or aging hard drive as much as from the lack of RAM.

You can upgrade RAM to 16GB and the HDD to an SSD if you like. The best RAM and SSD suppliers for the older Mac Mini’s are OWC and Crucial.

The thing you have to ask yourself, is it worth it to put money into say a RAM and SSD upgrade when it can only run 10.13 High Sierra, or is it better to put that money towards a new Mac Mini.

I agree with @den.ted in the fact that putting that much into a 10 year old machine may not be a wise move.

Personally I have a 2011 MiniServer that in the past I originally upgraded it to 16GB RAM and several years ago as I was upgrading other Macs that I had previously updated with SSDs and updated again to larger SSDs and the SSDs removed from them were put in the 2011 Mini Server. At this point in time, however, it is quite rapidly losing its usefulness as newer OSes, newer apps, are no longer supporting the hardware, even since it has been relegated as a media center.

Based on my experience, putting the money for a memory upgrade and SSD into a 2011 quite frankly would be a waste and that money would be best used toward a new or newer Mini.

In my experience with memories and ssd's (the latest since 2012) the answer is Samsung for SSDs and Samsung or Hynix for RAM.