6D would be wonderful, but will wipe out your entire budget.
A newer crop sensor camera also can be a significant upgrade and is very capable of making great portraits. What's the largest print you make from your images? Today's 18MP crop sensor cameras can make excellent 16x24" prints.
I'd suggest instead to go with 60D and put other money into lenses and lighting. There would be little to be gained going to 7D, for someone primarily shooting portraits.
Sticking with a crop sensor camera also allows you to consider crop-specific lenses, some of which are excellent, but smaller, lighter and less expensive than lenses for full frame. You actually have a wider choice of lenses with a crop camera (since it can use both FF lenses and "crop only" lenses... while a FF camera such as the 6D requires FF lenses).
24-70 is fine for your purposes. Definitely keep it.
Some primes would be nice. If you go with a 60D, because it's a crop camera, for portraits don't get longer than an 85mm. You also might want to upgrade to a better 50mm such as the 50/1.4. A wider lens such as 28/1.8 is useful for group shots.
Alternatively, if you stick with a crop sensor camera a wider zoom such as a 10-22mm might be useful... however for portraits you won't be using the wider end of it very much. There's too much wide angle distortion most of the time. The 17-55/2.8 would be a good replacement for your 18-55, if you don't need so wide a camera.
As to location lighting... well that's your call. There's a school of available light portrait photography, that only calls for reflectors, diffusion panels and flags. Or you can work with Speedlites. Or there are location lighting kits. Lighting is a fairly complex field that requires some study, practice, and may need some add'l gear such as a flash meter, various light modifiers, etc. You can easily spend $2000 just on lighting gear.
