What motive would Tosh Raka have to want to invade Tamriel?
I'm pretty new to any lore diving at all, so can some buffs give me a place to start?
Well, apart from there being previous Akaviri attempts:
Tosh R
aka -> R
aka Tosh -> Akatosh. Tosh Raka can be a mirror of Akatosh, an aspect of Akatosh, or even Akatosh himself, who knows.
The Nords of Skyrim refer to Akatosh as Alduin. Alduin is often referred to by the Nords as world-eater. Which is based in Nordic myth where Alduin destroyed the old world to create the current one, therefore the Nords see him as both creator and apocalyptic harbinger.
And Akatosh is off course also linked to the Empire. He was involved in forging the covenant with the Empire of man, his blood being tied to Alessia and the Empire with the amulet of kings being the primary token of that bond. Also, his patronage has the influence of maintaining the barrier between Mundus/Nirn and the planes of Oblivion. But now, it seems, that covenant has been broken. So Akatosh might be looking to renew the covenant, or to undo it all together.
I'm not saying that he is involved (either Tosh Raka, Akatosh or Alduin), but it would make sense, and it would give some interesting plot lines. It's all just healthy speculation.
As for lore diving, and a place to start:
A nice point to start for references is the http://www.uesp.net/wiki/Main_Page(<-click), but they often make assumptions in the lore that aren't exactly undisputed. Another great resource is the http://www.imperial-library.info/(<-click).
TES lore is wide and expansive mind you. Don't expect to get quick and easy answers. Expect to be more confused then ever.
[edit]
Why can't we vote for other provinces, maybe they could invade skyrim?
It could be that the dragons represent the empire of Cyrodil actually, with the Empire's draconic heraldry and it's patronage by Akatosh. And the Empire actually employed dragons to fight it's battles at some point. Dragons which have since vanished. So yeah, the empire is a possibility. But then again, it's all speculation. Only Bethesda knows for sure.