Modern Vespa

My VBC 1966 has 150 stock cylinder, 2 transfer ports, SI 20/15D carb, 8" wheels and stock exhaust.

Would it give more performance or at least better if I fitted SI 20/20 carb and bigger box exhaust?

I know 177 kit gives huge performance, but I'm not going for it now, and I'm wondering if I could achieve highest possible performance which stock engine can give through some tuning.

Yes.
I had a VNB 2 port engine and I installed a 20/20 carb and a SIP Road 2 exhaust.
The improvement was noticeable. Not a speed demon by any means but definitely faster and stronger on the hills.

Great, I think i'm going for it. Anyway is that the SIP road 2.0 with 2 securing bolt arm (idk whats it called) so the bolt go trough swing arm? cause I also found another with only single arm

I used the SIP Road 2 like in your picture.
My VNB doesn't have a exhaust bolt hole that goes all the way through the swingarm.
I just used the front tab on the exhaust to bolt it on just like the stock exhaust.

You will have to adjust your jetting once you make these changes.

Do you use bigger air filter for 20/20 carb? Like air filter for PX

If youre using a PX 20/20, definitely use a PX filter. That way the idle screw and body fit correctly.

How much $$ & time do you want to spend on it?

NOTE; my responses on this specific topic may have some bias.