Is first class worth it?

as my 2 suitcases about 70 - 80 cm high and maybe 45 cm across

and about 25-30 cm in depth

now the bigeest one with be empty as I will do shopping in JAPAN

so seriously can I get those 2 on the trains?

That is not too big. You might be able to put them besides yourself or even onto the overhead shelf.

Apart from that, you should consider deliver services:
http://www.japan-guide.com/e/e2278.html

Or a soft bag rather than a suitcase for the souvenirs.

I dont really want to use that as I want to go quite a few places I want to go

so every time I want to go somewhere, will cost me 2 suitcases every time