I'm not very familiar with Dr. Who (I just watched season 1 of the reboot and did not continue), but I can talk about TNG because I have watched the whole show (and I really like it). It's a long show (178 episodes over 7 seasons). Being episodic, each episode is a different story and there are stronger and weaker ones.

Yes, if you don't want to devote much time to it, you can watch the best episodes following whatever guide you want. The episodes are quite standalone, barring the occasional double episode, so you'll be fine sampling the highlights of the show that way.

However, there is something you will miss, because part of the charm of a long, episodic, ensemble show like this is the feeling of living with those characters day to day, so that they become almost members of the family, and following their character arcs. Even weak and campy episodes are enjoyable for me because of that. But, if you don't want to spend all that time, that's a reasonable trade-off you can make.

One thing you should know about TNG is that season 1 and, to a lesser extent, season 2, are considered weaker by most fans. Have you heard the expression "jump the shark" to refer to the moment when a show stops being good? It's an expression that was taken from an incident in the sitcom Happy Days. Well, the opposite expression is "grow a beard", to refer to the moment when a show starts being good. That expression was born from TNG, because during season 2 the character Riker grows a beard that he keeps for the rest of the show, and that's where fans say that the show started being good.

Personally, I also like season 1, although I agree that it has more weak episodes than other seasons.

This is a watch/skip guide. Just somebody's opinion, and I would personally recommend watching more episodes than this list suggests, but you could give it a go if you don’t want to watch many episodes: https://wordmerc.medium.com/star-trek-the-next-generation-watch-skip-guide-e489377bfd9

You could also look the the TNG re-watch at tor.com, and watch only the episodes that are given a 5 or more rating, for example (you can see the rating at the end of the write-up for each episode, just go directly there to avoid the spoilers in the rest of the write-up). It has the advantage that, having a rating, you can set the bar as high or as low as you want. Again, it's just somebody's opinion, and I often don't agree with his ratings, but that's a given when it's something subjective like this: https://www.tor.com/series/star-trek-the-next-generation-rewatch/