1-2-4-3
Right now there are some really good coaches available if you are willing to pony up the cash. Every offseason there's a whole host of free agent coaches that can fit your needs. Seattle is courting Rick Tocchet, Gallant was just a free agent coach, theres a handful of Claude Julien/ Torts/ Therrien/ Roy level coaches out there that could bring structure to your team until you are ready for a higher level coach (if you didnt see those guys as your long term fix). There's a lot of promising up-and-comers too, Lambert, Groulx, Gronborg etc. The problem isnt coaching availability, its teams not wanting to spend on coaches. Even though it would be the first hire, it would be the least impact choice long term.
I put goalies as second last because of long term indications. If you lock up your centres and d long term, in 5 years you'll still have a strong core. If you lock up a borderline goalie long term, you are in a heap of trouble. Over the course of your first few years, a lot of options to get a goalie will present itself through UFA or trades or whatever. Its an easier problem to fix imo
Centres I picked above D just because of how hard it is to get centres. D seems to be just a matter of draft luck + good predictive analytics (ie Vegas scouting Theodore and realizing his potential) but centres are really only mostly found through the draft, a team with bad D can gradually improve but a team with no centre depth seems bound for long term mediocrity.