When going out on a long exploration trip, the Number One advice is always to
fly the ship you're most comfortable with, and do a shorter test run first.
Would suck to eventually find that you can't wait to ditch your ship when you're 300 jumps away from the nearest shipyard.
You said you flew an Asp on DW2, so that would probably work. Compared to that, you'll find that the Anaconda handles significantly worse in supercruise, and you might not like the cockpit. (That's subjective, of course.) The increase in possible jump range might not compensate for that - after all, jump range only matters if you're in a hurry to fly from A to B, or when you're travelling to/through sparse areas.
Most ships can do 50 ly with a reasonable amount of engineering, and that'll get you almost anywhere. (Comparison: back when the top jump range was 40 ly, we still explored all regions of the galaxy. Especially once synthesized boosts became a thing.)
See
this thread for data on how exactly all the ships handle in supercruise, and
EDAstro has some pretty good comparisons between all the ships. (However, note that the SC figure there only uses pitch, not yaw nor roll.)
NS boosts won't damage your power plant (nor your hull), everything else can be avoided if you pay some attention. Best to rely on yourself first, not engineering.
One more thing that nobody mentioned here: heatsink launcher. I've been exploring since the game was released, and I only had to use it once (jumping through a star and immediately overheating from the two stars), but the launcher can be engineered to weigh next to nothing. Even the base 1.3T won't impact your range much, unless you're flying an Imperial Courier.