> I guess that *this one* is not the right one to start with...

No, not a good first LCD project. A more standard one
with a 44780 interface would be much friendlier to work
with. A 16x1 will usually have just a 44780, 44100s are
added for more lines/characters, the appropriate one
getting its information from the 44780 via the value in the
address register

Some time ago I bought a load of surplus ex-FedEx LCDs
(I think they were off parcel scales). Big 4x40 quad-height
backlit screens, very nice. They have no controller chip, just
NEC D7227 segment drivers. Still not got around to fully
programming a PIC as a controller. You'll also often find
old laptop LCD screens that have just a dozen or more
44100s or similar, control coming from the mobo

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