I have only done a short trip (2000ly round trip to Barnard's loop) but exploration arent dangerous apart from two things, crashing into suns or running out of fuel, but this is true for k-space as well.
Don't stress it, do like Kirk. Pick a direction and go
Having good jump range is great but only a must if your going to the edge.
Get a great fuel scoop , biggest you can fit and afford, less time spent scooping is less heat exposure faster travel, this an the advanced scanner pays for itself, and you get your money back when you sell it.
In fact only time anything costs anything in this game is if you die and pay the insurance, or the 10% loss from ship sales.
But go for the sights, not the money, never be afraid to make giant detours for shiny things
Take your time and take screenshots of whatever you fancy.
The asp is the defacto explorer because pre 1.3 it had the mix of a big tank, the fsd is somewhat oversized so you get great jump range and distance, after 1.3 we can add extra fuel tanks so even a Sidewinder can get to a 100ly range between refueling stops. And it could fit lots of various extra modules like field maintenance kits and heat sinks.
That said you only need heat sinks if you screw up, and you only need the AMU'S when you have screwed up on multiple occasions.
Ship integrity is something you can just forget about, it will decrease from hypercruising no matter what.
Even if it gets to 0 it just means your total Max hull strength has decreased by 30% you won't risk decompressing or anything.