Hi FF,
Well, firstly it's been a few years since I stopped working with EFB's but - I think generally the terminology (at least in the EASA world) these days refers to either 'Portable' or 'Installed' , the former being the Type I & II equivalent and Type III being akin to the 'Installed' scenario.
When it comes to software - well, by way of example - Airbus utilises (for performance, W&B, FCOM etc) the FlySmart (FS+) suite of applications, and Boeing uses Boeing OPT - both applications being very intuitive and user-friendly in the main - I am biased towards the Airbus offering, but that's perhaps only because I fly on the 'bus. for other documentation, and if you have access to created .pdf forms, or the ability to create like I do - then Readdle's 'Fluix' is a very cost effective and easy-to-use application, and allows all sorts of workflows (now with API's, even better!) and annotation abilities, form submission routing to name but a very few - well worth a look. For charting, again Jeppesen's 'FD-Pro' is almost a defacto standard, or LIDO (no experience with the later). A good MDM solution to manage your companies EFB programme (VMware - AirWatch?) is also highly desirable if a larger set-up and allows for control over deployed devices and updates, when gaining approval - stuff like this will make your life in gaining approvals so much easier.
With getting approvals - it always used to be (when I started) the NPA-2012, which became AMC 20-25 and has now moved to something like - PartSPA.EFB.100 - do a Google search for the EASA Easy Access Rules, and you'll find it pretty easily. Oh, and various application manufacturers will often have software EASA evaluations available, along with a lot of software conformity certificates, user manuals, and alike.
Naturally there is a whole lot more than the brief areas I have mentioned, but should give some ideas I hope?