Well, something like Fighter 1/Wiz 5/Eldritch Knight 10/Wiz +3/Fighter +1 is about as simple as non-monoclass builds can get, being Core only even, and still achieves 9th level spells and BAB +16, but is also pretty damn playable throughout.

In the end, SBS (and that's a neat acronym for it) has sharp drawbacks: your spell choices are absurdly tight, and spells are still your only class features. But it can't be said that having access to even those very few, but appropriate in level for a full-caster, spells don't make it strong by the end.

One just has to be aware of things like "your spell repertoire is one level 1 spell until you hit level 4".

But by mid levels, as long as you think of your guy less like a sorcerer and instead like an ok fighter dude with some superpowers, it can be pretty sweet. By 8th, you can attack twice on a full attack like all the cool kids, but you can also become Greater Invisible while you Fly and hit people with Schorching Rays in between bouts of swording. Gishes tend to look really good in what 5E calls Tier 2.

I think that mentality of "I'm not a sorcerer, I'm a sword guy with powers" is important, so perhaps not walking around with the usual suspects of Wizard, Cleric and Druid would help. You should fit right in with Bards, Rogues and Warlocks tho.