Thinking of buying a 556 Classic

Unfortunately I've seen bad examples throughout the run of the US Sig 556 rifles. However, 2009 production JT serial rifles seem to have the worst fitment / function issues.
The first run rifles (ER or Early Release) are some of the very best IMO but the top rails can be canted a bit.
You are correct, though. The serial circa JS034200 would be 2nd gen. Definitely do a thorough check before you purchase. Perhaps even ask to put a few rounds through it before you buy, if possible.

I have a JS023XXX and its good to go! Has some Swiss internals. Shoots good.

That folding/collapsible stock sucks. It wobbles like crazy. So you're going to want to replace it with the standard Swiss folding stock which is rock solid. I'd plan on buying a swiss rear diopter sight as well.