I think you've gotten tangled up in too many people's optimization theorycrafting. This will be a, in some ways, suboptimal character, and that's fine. It'll still be a 5e Wizard, and unless you dumpstat intelligence or just can't pick a spell to save your life, that will always be a powerful enough character to meaningfully contribute to the party. Personally I wouldn't advise being an unarmored Wizard without a 12 or 14 dex, but if you really can't spare the stat, do what you must.
Is mage armour worth it at low levels, or is the difference between getting hit all the time at AC 10 and getting hit almost all the time at AC13 not worth the expenditure of one of my very few spell slots?
If you have no other armor Mage armor is probably worth it at low levels, even with crap dex. Lets say you run into a gaggle of Goblins. Some will target the wizard with their bows. They have +4 to hit. With a 10 AC they hit on a six or higher (75% chance). With a 13 AC they hit on a 9 or higher (60% chance). Still bad, but you can also use Shield, bringing it up to a respectable 18 for one round in an emergency. If you win initiative you'd be better off using that spell slot to hit the Goblins with Sleep, but if you lost initiative (more likely with crap dex) you've got to focus on surviving. At level 1 you're probably only good for a couple hits, so anything that even marginally lowers the chance of them landing is generally a better use of your level one spell slots than any of the anemic level 1 damage spells. That said, if you can drop a whole group of gobbos or kobolds with a Sleep spell, or avert the fight entirely through some sort of Disguise Self/Charm Person/Silent Image shenanigans those are more effective use of your spell slots. Tough calls.
But whether or not you can afford spell slots for Mage Armor or Shield (or Absorb Elements) at Wizard levels 1 or 2, you absolutely should pick up the spells during those levels. At level 3 and beyond level 1 slots become a lot less precious, and these low level defense spells increasingly become the primary use of those slots, and since the eight spells you pick at Wizard levels 1 and 2 have to be level 1 spells, you'll want to grab the defensive spells then. Whether you actually prep or use them yet will be something to play by ear.
Is it practical to pick up the much-maligned Blade Ward and at low levels trying to rely on reaction spells like Hellish Rebuke?
Blade Ward is an interesting idea for this build, as in not as terrible as it is for most, but I think the "accept you'll get hit, and give up your action to lessen the impact" strategy doesn't really make sense even for a high con, low dex Wizard. You don't want to invest one of your 3 known cantrips on something that is usually not a better option than taking the disengage, dash, or hide actions. I might consider it later in the game when you're learning your 5th or 6th cantrip. Hellish Rebuke is a Warlock spell, so you won't be using that.
Should i just bite the bullet and go fighter or barbarian at level 1 for the armour proficiencies, and then multiclass into wizard?
Both solid options. Keep in mind the only one of those that actually grants heavy armor is taking Fighter
at level 1. Medium Armor is certainly also nothing to dismiss, even with crap dex, but if you are going to devote a whole level primarily to shoring up your AC, you might as well go for the best you can get. Fighter also gives a fighting style to increase your AC by yet one more and Second Wind for a little self healing when you do still get hit. If you take one level of Fighter then someday you can take a second, and Action Surge double spells.
Barbarian is definitely less optimized, but still very cool, gets the job done, and would make for a generally very survivable character. At low levels raging when you run out of spells makes a lot of sense. A second level someday would let you attack recklessly with those horns. Unfortunately as your wizardry eclipses the power of your melee attacks the benefits of a Barbarian dip start to diminish, so I really wouldn't advise the second level (unless your DM lets you use your horns with the Booming Blade cantrip, in which case those horns might get a lot of use, and being able to use them with advantage radically ups their viability).
For the character to make sense I would talk to the DM about letting you start already having your spell book, and just not being able to use it yet. Maybe you found or inherited it, or maybe you were a Wizard school dropout who focused too much on sports and never managed to cast any spells.