One of your questions not yet fully addressed in this thread is the question of "Where to go?".
The answer depends to an extent on what, exactly, you want to get out of exploration.
Do you want to make lots of credits and/or quickly gain an Elite rank so you can unlock the Founders World permit? Then the "Road to riches" guides will help you get max credits for minimum effort. This isn't "true exploration" as Road to Riches uses planets already discovered by other people, but it counts as "exploration" as far as the game is concerned.
Do you want to fill in the Codex checklist of Things to See? Simple - just go to the systems and planets the Codex says to go to, and you can check the things off one by one. Again, not "true exploration" as you're finding things other people have already found, but if you want to see the variety of content there is to see in the game, using the Codex to find it is usually reliable, and you can probably get plenty of "true exploration" done enroute between Codex entries.
Do you want to see the glorious nebulae and spectacular giant stars you read about in the real-world news? Again, you're not the first person to want to see the biggest and boldest, so all such galactic features, if they are in the game at all, are thoroughly explored by now. Still good for epic screenshots, though.
Do you want to simply plant your flag on as many stars and planets as you can? Then you want to head out into the Unknown regions, far from the regular space lanes and tourist routes. Or, head deep into the Galactic Core - stars there are so densely packed together that even the heavily trafficked routes are still jam-packed with loads of Unexplored stars.
Do you want to find Earth-like planets, future homes for humanity? There are things you can do to maximize your chances of finding ELWs - selecting just A and F class stars and deselecting everything else in the star class filter is a good way of finding the most "valuable" systems, in terms of finding Earth-likes and Terraformables. It's kind of a "make your own Road to Riches", not quite as convenient, not quite as efficient in terms of credits per hour, but much more satisfying, as you're doing "actual exploration" - and planting the flag with Tags and Maps.
Do you want to find the rare, the interesting, the extreme edge-cases of the Stellar Forge, the things that make everyone who sees it go "Wow!"? Sorry, but there's no easy way or tips for finding those. The Stellar Forge is effectively random, and there's no way to predict such randomness. It's just a matter of constantly asking "I wonder what's in the next star system?"... and making that next jump to see what's there.
Suggestion: don't head way out to the outermost reaches of the galaxy. "Circumnavigating the galaxy" by flying out as far as any ship can reach, is a highly popular pastime for many "boldly going" explorers, and with star densities so low and traffic so (relatively) high, it means that the "galactic circumference" is quite thoroughly explored by now. Ditto with Beagle Point - people who go there and back again are "long-range travellers", but not really "explorers".
Or, to put it another way:
In the Spoiler tags is a link to the most excellent EDAstro heat map of explorability, created by Cmdr Orvidius: an estimation of the thoroughness of current exploration efforts to date. Red is "thoroughly explored", black is "almost completely unexplored". To be a "true explorer", avoid the red, white and cyan zones, and head into the blue and black.