If your goal for modelling is explanation (just humans reading the views) you can use anything that makes it clear. If you want automatic analysis, you need to decide on a set of fixed patterns to model everything. Make sure you think beforehand about possible uses, because a minimally viable first set is a lot of work to expand later.
Modelling data transfers has become easier with ArchiMate 3 as you can link Flows to objects. Before that, you could use Access with Data Objects and let those Data Objects Realise Business Objects to tie the Flows together. But you need a tool that can do programmable analysis to really make use of such a model.
And yes, I’ve done this (modelling the entire landscape) with my team (>75,000 elements and relations in a single model, I know of larger models) and I’ve written a book about it :-) :-)
G
PS. Note that in landscpae modelling like this, there is not a single view (not really doable or usable), but there is (can be, there are uses where you ave multiple) a single model with multiple views. That is something that is not easy to do in Visio (you probably can with some extra tools that link Visio to a backend, but I’ve never done that).