Upgrades to my stock 273 67 Dart GT

Ignition first, hands down. Just don't get suckered into one of those all-in-one cheapo internet distributors- more problems than they're worth. Get the actual Mopar wiring conversion kit, a good ignition box (avoid the "orange boxes", lots of issues in recent years. In your situation I'd get something like the Standard LX101, solid and reliable), and a distributor with a nice advance curve built into it from @halifaxhops.
From there, follow up with good wires, a quality cap and rotor, and plugs of course.
And don't forget to set your valve lash- who knows how long it's been and could be a good ways off.
Then attack your wiring (you did say reliability was important). Clean all your connections at the bulkhead connector, at the components themselves, and get all your grounds squeaky clean and tight. You'll thank me later- any performance upgrades you do in the future will only work if the engine starts and runs consistently...
Then upgrade your alternator and voltage regulator to the later electronic type. Do a search in the electricals forum to get the lowdown on how it's done.
Then duals from your exhaust manifolds. The HP single is awesome, but pricey- you can get duals done much cheaper.
As far as intake/carburetion goes, initially I'd just rebuild the 2 bbl. As previously stated, a 4 bbl. swap entails other details like the throttle and kickdown linkages, and adapters for the throttle lever, etc. A good running 2 bbl. will give you good street manners and still be adequately peppy until you source all your 4 bbl. pieces. And as you source those pieces, don't forget some used out of production pieces like the Eddy Streetmaster 318, SP2P, or Holley Street Dominator- all of which work quite well on the little 273 and are generally more affordable due to their lack of desirability for bigger engine builds. As for a carb, a 500 Eddy would be about right; although anything up to 600/625 will work just fine- pick your poison, Holley or Edelbrock/Carter.