Based on what I remember of the “classic” Star Trek series:
TOS: can be watched in any order; very episodic; IMO has generally aged poorly and is not a good place to start
STNG: has a few plots lines through the series, but these only appear in some episodes; mostly episodic. If you’re worried about getting bored I think you can just watch the first two episodes, then skip to season 3 or 4. Once you feel like you’re enjoying the series go back and watch the episodes you skipped.
DS9: has a number of plot lines through the series, somewhat episodic, but best watched in order. The first season is ROUGH. My favorite of the classic series, but oh wow does it take a while to get good. Watch after STNG to understand properly.
VOY: pretty episodic after the first few episodes, with the exception of seasons 3-4 which have a fairly substantial continuing plot. The series makes a little more sense if you’ve seen season one of DS9.
ENT: has a decent amount of continuing plot lines, but still generally episodic. A prequel so it can be understood without watching any other series, but it has a lot of callbacks to previous shows that make it best watched last IMO. Also it’s probably the worst of the classic shows (excluding TOS which gets a pass for cultural relevance reasons), so I definitely wouldn’t start with it. I don’t think any one season is especially better/worse, and it’s fairly short so there’s not much point in jumping around.
In conclusion, I’d recommend either starting with one of the newer series, or watch the first two episodes of STNG, skip to S3 or S4, then once you’re enjoying it go back and watch STNG in order starting from S1E3.