I hope you don't mind me chipping in here.
I am going off your statement that you'll mostly be shooting interviews/videos with loads of talking about nutrition products (Funnily enough, I've shot similar stuff and got a job coming up, but with a lot higher budget, so I am hiring a sound guy).
1) Cut out the slider, save 350 bucks. Why do you need a slider for a simple talking head interview? I don't believe that you need sliding shots, especially if you only have 10.000 dollars to spend. (I am not against sliders, I own a Kessler Pocket Dolly and a 6 foot Shuttlepod myself...)
2) The Blackmagic camera is not a bad idea, but have you considered your lens choice? Yes, you have a fast lens and a lens that would be a good medium wide on a 5D, but bear in mind the crop factor of the Blackmagic camera. With a 24-70 you wont be able to get decent wide shots which can be very important (especially if you want to use a slider).
3) Have you considered power for the Blackmagic camera? You need to buy a V-Mount and V-Mount battery to power your camera for a decent amount of time. Pausing a shoot and waiting for your camera to charge will get you booted off the job, quicker than you can say "I have to charge my camera".
4) Buy the best tripod you can get for your budget. If all you really want is to support a Blackmagic camera or similar in weight, buy a Sachtler ACE. Much better than cheap Manfrottos.
5) Invest in SOUND! I 100% agree with Alcove, sound is very important. If you only record with a shotgun mic, you will get less than optimal sound. I shoot a LOT of talking heads and corporate films with interviews and my lavalieres have been the best thing I've bought so far. There's a lot of different mics for different prices, but buying a lavalier mic is the first step to good sound. I use the Sennheiser G3's a lot and own a Sony UWP-V1 system which I often use with a TRAM TR50 mic. The standard mic (the one that comes with the UWP-V1) is also decent, but kind of big. I always boom a mic on interviews as well. This is just a backup in case my wireless lav picks up any weird sounds/gets interference from somewhere. Most of the time I do this with a stand/C-Stand. Consider an audio mixer and a decent recorder as Alcove said. The H4n is not a really great option, there's much better out there, but I'll just let him advise you on that!
6) I know you're going high quality as "eff", but do you really need to shoot Cinema DNG or ProRes in 2.5K for a final output to an online medium? I don't see the point in this. It's gonna cost you a lot of money in SSD's (You have 760 budgeted for this) and a lot of pain in post production.
7) I am wondering whether a camera like a Sony FS100 (even used) would be a better solution. Depending on the quality of the audio you really need, you could even send your sound straight to camera. This is what I always do, because I don't have the time for dual system sound. I get 5 minutes to set everything up and then I have to roll most of the time.
What lighting will you use? Tungsten will give you the best colour rendition and won't give you any nasty colour spikes in skin tones for example. Tungsten lights get hot though, so your talent will feel uncomfortable soon. Have you thought about that? You don't want your talent sweating.
I use LED panels. 1x1 LED's by F&V Lighting. They're very cheap and you can pick up a 3 light kit which includes amazing diffusers for just 1000 dollars. This is super cheap for a light kit that gets the job done almost every time.
Anyways, think about a few of these things, as they can save you hassle later on. You don't want to end up with bad sound or a ton of work in post, just because you bought something not suitable for the job or didn't do much research!
