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Most explorers point their ship towards the primary star while the scans and system-map-loading are happening, to get a DSS of the star (and a Tag on it, if it's never been Tagged before).
+1 rep for all of this. Very standard procedure.
As to what's worth scanning, versus skipping, that's a whole separate conversation, and there will probably be very little agreement among the explorers. Some people like to scan everything (completionists), but that means spending an awful long time in supercruise. Some people prefer to cherry-pick and go after only the highest value planets (earth-likes, water worlds, and ammonia worlds, and possibly class-II gas giants). Some people prefer to scan all of the High Metal Content worlds, so that they can get the terraformable bonuses. You can learn to get a feel for where the habitable zones tend to be for each star class, but you can't know for sure whether the planet is terraformable until after you scan it, unfortunately.
Earth-likes and water worlds tend to be easy to find around class F,G,K stars, but the larger ones (O,B,A,F) tend to have wide habitable zones, so they can earn a lot of money from the HMC planets. M-class stars tend
not to be big money makers, but they're numerous and everywhere, and quick to fly around for scooping and jumping. Personally I will filter out M-class stars if I want to make money (or make the route planner work better when near the core, due to star density), but I'll include them (or use them exclusively) when I want to travel quickly. Near the core I'll often filter down to just F,G stars, and widen the selection the further from the core I happen to be. I always recommend letting the filter include the "bottom four" selections too (such as non-sequence stars (black holes, neutron stars), carbon stars, etc), due to their rarity and/or level of interest.
But all of this comes down to a matter of preference, and what your goals are.