I love this archetype! I'm playing one in an upcoming game.
Here's what I see each class giving you(alphabetically); (your list was good but I think you missed some important ones)
Cleric (tempest)
Heavy Armor Proficiency
For free even when multiclassing, big stuff if you plan on being up-close.
Spells
Thunderwave
Shatter
*Call Lightning
*Devastation Wave
*=exclusive to this class for this discussion.
Channel Divinity
Maximizing damage on an aoe spell is just bonkers, it honestly feels like cheating. At level 6 you get to do this 2 times a short rest!
Wrath of the Storm
A nice reaction to do some decent damage in either thunder or lightning.
Thunderbolt Strike
Free knockback for all you lightning damage! No save at all and it doesn't even have to be a spell!
Sorceror
[Saves]
Con Saves!!! By far the reason to start in sorc if you plan to multiclass into it at all, Con save proficiency is so valuable a lot of mages take Resilient to get it and you can start with it for free!
Metamagic
Quickened is amazing, heightened and empowered really hurt, careful is really nice for your allies as a lot of your stuff is AoE.
Spells
*Shocking Grasp, *Thunderclap, *Lightning Lure
Thunderwave, *Witch Bolt
*Lightning Bolt, Shatter
*Fly
*Storm Sphere
*Chain Lightning
Dragon-origin
Extra Health and natural armor
13+dex and +1hp/level is fantastic and definitely shouldn't be overlooked. That said it is only for sorc levels and the armor only really helps if you have a high dex.
elemental damage
The real reason we are considering this class; 3-5 damage per spell. They have clarified that even if this hits more than once it will only add the damage once. This is relevant for Storm Sphere, Witch Bolt, and Call Lightning, overall a good ability but is reliant on your cha.
Storm Sorceror
Free flying
A bonus action for 10' with no OA's is wonderful, usually that means disengage+extra movement.
Heart of the Storm
This can do 3-5 damage, to everyone you choose within 10' of you. That could be everyone you hit with that Thunderwave, or it can be people you couldn't hit. Generally if you are getting in the mix as a storm mage then this will do just as much, if not more damage than the draconic origin feature. It's also Lightning Damage! Which means if you have Thunderbolt strike you get to push them 10' no questions asked(neither has a to-hit or a save).
Wrath's Big brother
It is a looong way in at 14 but you get an excellent reaction, lightning damage=your sorcerer level. So 14-20 damage as a reaction, at base that's the same as 2d8+5 on average, and much more consistent.
Things to Consider
Unless it is a really hard-coded character reason I see no reason to use a melee weapon at all. Shocking grasp will easily out-damage melee weapons for you because of no extra attack, and often thunderclap will do even more than that.
Your role;
Are you a tank? are you a blaster? both? something in between? There are definitely ways in this shell to be near impossible to kill while still dealing massive amounts of damage back(this is the route I plan on going).
MAD;
If you are using a weapon/ wearing heavy armor and not being a hill-dwarf you are going to need a decent str.
If you don't want to die/lose concentration you need a good con.
Your damage will come from cha/wis or both.
that's a possible 4 stats you need to be decent, that is going to be really hard.
Dragonborn gives you some str and cha, so as long as you have a spare 13 you are ok on str(15 means no slow-down in plate).
Wis is important for cleric but not back-breaking at a +3 so 16 would be just fine.
Cha is where a lot of your damage comes from in the form of cantrips and spells so you are going to want to max this out, or at least get to a +4.
Con, this is where you have a choice, personally I am maxing this first, I'm going front-line and need the health and concentration to stay alive and keep blasting face. If you can find a way to avoid damage feel free to do lower, a +3 would be the minimum imo though, losing concentration sucks.
Personally the best in my opinion is either 14/6 or 11/9 Storm sorc/temp cleric.
You get the crazy thunderbolt strike/heart of the storm combo. You get heavy armor and max damage from cleric really early and going only 6 in you get 2 channel divinities and only miss out on Devastating Wave, which is good but I'm not sure it outweighs the reaction from sorc. You also get the wonderful saves and metamagic from sorc, you get cantrips so you can ignore melee weapons and some really nifty flight. I also think tanky is the way to go, you have heavy armor, shields and a good con, that's all you need to be a pain in the butt to kill, add on Shield and Blur if you really want to and you'll be a DM headache in no time.
If I was playing your character I would do 6/2 Sorc(storm)/cleric, level 1 in sorc, and go 7/2 next level so that you get Storm sphere asap, it's a big deal. This will keep you close to par on spells-known too, after 9 I recommend getting to 6 in cleric for thunderbolt and call-lighting, by 13 7/6 would be my goal.
That said this is your beast, I hope the information I added helps your decisions!