I don't see how an incursion on Ukraine would result in a war with NATO. Ukraine's problem is precisely that it's a formerly neutral party and not part of NATO. In fact, from a Russian POV the reason for the annexation of the Crimean peninsula were fears fueled by Ukraine moving closer to NATO and the EU, violating its neutrality and jeopardising Russian military operations within Ukraine.
I'm not justifying the annexation -- it was clearly illegal and the circumstances of the (also illegal) vote suggest fraud -- but Ukraine is not part of NATO and even an all-out undeniable Russian invasion wouldn't trigger a war with NATO.
Is it in NATO's interests if Russia fully invades or goes to war with Ukraine? No, of course not. Is it a violation of international law? Most likely so. But would this trigger any international treaties that would result in WW3? Hell no.
WW1 and WW2 weren't just escalated because The Good Guys were unhappy with the aggressors. They were escalated because of international treaties forcing nations to declare war in retaliation to the aggressors.
In WW2 the invasion of Poland triggered the defensive pact with Britain and France who declared war after setting an ultimatum. As for WW1, I think most people have heard of the complete clusterfuck of international alliances and naivety that resulted in that escalation[1].
Ukraine is not part of the EU. Ukraine is not part of NATO. Strategic position aside, there's little reason for NATO to get involved as long as Russia has no intentions of moving further westwards. Even if the US invaded directly and declared war on Russia this wouldn't trigger NATO as NATO is a defensive pact, not an aggressive pact. It would of course result in a lot of diplomatic tensions with so many US military bases being located in the EU.
[1]: https://en.wikipedia.org/wiki/July_Crisis