Suggestions would be great.
Plain white shirt, solid navy tie (some texture, like a grenadine or repp, would be nice, though satin could work), black shoes.
Could you wear a patterned tie? Of course, but if you're not confident in pairing patterns, then a solid tie will be the more elegant, safer choice. If the PS is predominately navy, then wear a solid tie in burgundy or perhaps a very dark green to avoid a near-match.
If it were day time, then you'd want to avoid the satin tie, possibly try for a patterned tie, and consider a blue shirt and brown shoes.
When I wear my squares that are printed like that, I generally pick one color to show, because I don't like how the hard line between different quadrants looks.
I'm not sure about the tie choice -- it can be tough to wear a light tie with a light suit, and if it's a very light blue, then the square would have to be darker. That wouldn't work well for me. If your tie was darker, and you arranged the square so the lightest part showed, then I'd be on board 100%. As it stands, I think the light tie/light suit would be best with a white linen square, though I like the idea of a light blue dotted square with a solid tie.
The socks sound like a nice choice, and a pair of brown shoes is perfectly acceptable -- particularly if they're more elegant than whatever black shoes you own. If you do have a particularly nice pair of black shoes, this is an excellent context for them.
Given how gray the lightest blue in that is, you might want the second lightest to show. The tough thing with pocket squares is that you don't want one that blends in with your coat too much, but you also don't want it to be the only dark thing in a rig (light tie, light shirt, light suit).