Giant crx four going from 30c to 32 width.

I am currently runing 700x30c and the clearence looks like this [IMG]freeimage.hostimg 20201001 010813.2E6m9pOpen ↗[/IMG]
I seriouly want to get good puncture resistance tyres so i was suggested to look at tyres like Schwalbe marathon plus, gatorskins, armadillo etc. I foud most of these tyres are either 28c or 32c. So, I made my mind to get 32s because they would fit on the rims (Alexrims Ace 17) but can I get some clarification on two aspects. first, would I need a bigger tube for a 32 tyre and secondly, would the tyre actually fit? This bike has been discountinued and I cant find information on their web.