Strange New Worlds is probably the best start. I like Discovery a lot, esp. since it kicked off this new age of Star Trek, but it is a different format than you'd usually expect from Trek, thus the outcry. Strange New Worlds takes the classic Trek formula (which is not a bad formula--there's a reason it has legs) and updates it with modern values/stories/special effects/etc.

Older Trek is massively nostalgic for many, but it's also massively uneven in quality as they were churning out seasons on a shoestring budget and it often shows. Also, they didn't always correctly predict how tech would go (esp. computer tech) so you can have things that are plot holes given what we know of technology today. If you want to start with older Trek, I think the Star Trek Next Generation movie First Contact might stand well enough on its own, esp. if you cherry-pick the Borg-related episodes (there's only a few) from the TV series and watch them first.