Mac Mini Upgrades - Recommendations?

8 GB of memory will do as good as 16 GB of memory. Only if you use applications or run programs which require a lot of memory you would notice any difference. Such cases would be graphics, DTP, audio etc. Also running more than one VM e.g. in VirtualBox would make more memory necessary. Otherwise: 4 GB are okay, 8 GB are well. 16 GB are exceptional.

You may need to reset the PRAM/NVRAM after a hardware change: https://support.apple.com/en-us/HT204063

To clarify: even though Apple officially only supports 8 GB memory on this Mac, I have personally tested it with 16 GB in Mac OS X 10.6.8, Mac OS X 10.7+10.7.5, OS X 10.8+10.8.5, OS X 10.9+10.9.5, OS X 10.10+10.10.5 and OS X 10.11+10.11.4. My Mac mini is a Macmini5,2, i.e. the 2011 model with 2.5 GHz and a Radeon 6630M graphics card. (Yours is a Macmini5,1 with integrated Intel graphics.)

An SSD will considerably speed up the Mac mini 2011. Also, there is a dual HDD installation kit available, so you could use a 512 GB SSD and a 1 TB HDD for data. (Or, if sufficient, a 256 GB SSD and a 512 GB HDD.) https://www.ifixit.com/Store/Mac/Mac-Mini-Dual-Drive-Kit/IF171-005 You can also find this kit in other stores, even Amazon.

Be adviced: when using an SSD, turn on TRIM using either Trim Enabler or forcetrim. http://osxdaily.com/2015/10/29/use-trimforce-trim-ssd-mac-os-x/

That’s about it. There are no more upgrade possibilities for this Mac, except for an external Thunderbolt 1 device or USB 2.0 peripherial devices.

You haven't said much about your attached storage. The internal drive is a slow 5400 rpm drive, unless you have already upgraded it. The amount of disassembly required to swap in a new drive may be more than you want to do yourself, but you could buy the drives and pay an authorized Apple service provider to do the installation.

The Adobe apps use a lot of whatever free disk space you have for caches and saved states: it's one of the things that allow InDesign to recover well from crashes (at least in the versions that I have used) and Photoshop to have history states to which you can revert. A nice big external drive would help with that. OWC sells an enclosure that is the size and shape of the Mini, and might be worth considering if you care about stacking the Mini and the external drive. It comes with FW800, which would probably be your best option in terms of speed.

https://eshop.macsales.com/item/NewerTech/MSQKIT0GB/

Install a 4TB drive in that, such as a 7200 rpm HGST or WD Black.

Caution with that! Drives that are 12.5 mm high won't fit! http://www.tomshardware.co.uk/2.5-inch-12.5-mm-9.5-mm,review-31902.html

I assume you mean the internal drive. So the OP needs a 9mm high 2.5" drive.

https://eshop.macsales.com/installvideos/mac_mini2011_hd/

The enclosure in that link is for 3.5" drives, and they do fit in there.

I'd suggest investing in a good enclosure and adding the drive of your choosing to it. Some skimping goes on in brand name externals from Seagate or WD, etc., in terms of the quality of the enclosure. And you don't know exactly what drive you are getting. The OWC enclosures make it simple for anyone with opposable thumbs and a screwdriver to swap drives in or out of an enclosure. This is important for trouble-shooting a problematic external drive. You need to be able to determine whether the drive itself is failing, or whether the enclosure or the cable could be at fault.