D&D 5E I want to be a tough full caster

I like the Mountain Dwarf Draconic Bloodline Sorcerer
medium armour or (13+dex)
1d6+1+con(3)hp or 10 hp lvl 1 and 8 per level (a 14 con fighter gets 8 hp per level)
proficiency in con saves for concentration with massive con backing it
twin spell allows you to apply powerful single target buffs or debuffs to 2 target and concentrate as if it's one spell.
decent melee back up with dwarven weapons and AOOs
feat Recomendations (+2 Cha, War Caster, +2 con, Inspireing leader, Durable) other options (mage Slayer, mobile, medium armour master, +1 con +1 dex)
18 cha
15 con (becomes 17)
15 dex to get your best AC from the medium armour
10 wis
11 int
12 str (becomes 14)

edit
and using low level spell slots for sorcery points for higher level spell slots or quickening a spell.

Leatherhead said:

Imo, warlocks aren't full casters.

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After playing one the lack of spell slots makes me agree you are 11th level before you can cast 3 spells between rests. Though the cantrip spam can be fun.

A Hill Dwarf (+1 hp/level) Wizard and a 16 Constitution gives you 10 starting HP. That's plenty.

A Mountain Dwarf Wizard and a 16 CON gives you 9 starting hp and Medium armor proficiency.

You can't go wrong with Dwarf Wizard. ^_^

Leatherhead said:

Imo, warlocks aren't full casters.

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They are kind of like a 7/8 caster - they get the highest levels of spells so they are close to full, but without the day going just right for them they cast non-cantrip spells less often than other classes that are full casters could (well, assuming their invocation choices don't bridge the gap, at least).