MinION is an option. However, it actually depends on the intended application. Also things like length of the read, accuracy of the read, throughput etc.
I'd like to expand a bit on this, especially as the EMBL article is fa bit older. For the record, I do not have any affiliations to Oxford Nanopore Technologies, Pacific Biosciences, or Illumina. I am just highly interested in long read sequencing.
The MinION has come a great way and is now applied in remote environments (http://biorxiv.org/content/early/2016/09/07/073965, https://www.nature.com/nature/journal/v530/n7589/full/nature16996.html). If you want a bit higher throughput, the GridION X5 (https://nanoporetech.com/about-us/news/introducing-gridion-x5) could be of interest. Moreover, the SmidgION, a mobile-phone attachable sequencer, might (one day/soon) become available (https://nanoporetech.com/products/smidgion).
With respect to long read sequencing in general, it should be noted that the library preparation is an absolutely crucial step and is probably not as straight-forward (yet) as it is with more established sequencing solutions, e.g., from Illumina. The providers (Pacific Biosciences, Oxford Nanopore Technologies) are however working on that front with rapid protocols and low-input protocols becoming available and getting improved constantly.
Depending on what is considered "mini", the Illumina NextSeq might be an option. It is however "benchtop"-sized and produces short reads.
Best,
Cedric
P.S. For completeness sake, and although it is far from "mini", if you are interested in long read sequencing more generally, Pacific Biosciences might be worth a look too.
P.P.S. In general, if you found an answer helpful, please consider clicking on "Recommend".