I have that camera. Here are a few things to consider:
The camera doesn't have any in-body stabilization, so the footage can be very shaky unless you're prepared. In my situation, I knew I wanted to use a gimbal to stabilize. This works great, but it will affect your lens choice. If you plan to use the BMPCC on a gimball ever, remember that you won't be able to touch the lens to focus it, change iris, or zoom without disturbing the gimbal operation, so if that's in your playbook, you'll either need a remote follow focus setup (for a prime lens), or a lens that can be controlled remotely through the camera's bluetooth interface (for an autofocusing and/or stabilizing photo lens). Keep in mind the autofocus on this camera is very slow, and not very "auto." You have to tap the screen to re-focus unless you use bluetooth or remote follow focus.
When you say that you plan to use the BMPCC on a "Rig" I assume you mean shoulder rig. Consider how you are going to monitor the footage and control the camera with it on your shoulder; if you're planning to use the camera's built-in screen, the camera's center of gravity will be VERY (entirely) forward. Without proper counterbalance, you're better off not using a rig at all. With a properly balanced shoulder rig, you can just about let go of the thing with both hands, and it should stay balanced on your shoulder. There's no way to do that with this camera without an EVF or, like I said, some serious counterbalancing, which will more than double the total weight of what you're carrying. With a shoulder rig, it's possible to grab the focus/iris/or zoom ring, and you won't shake the image as much as you would on a gimbal, BUT it can be very awkward to reach, and it's better to have a follow focus setup with remote hand grip controls in this situation as well.
The crop factor on this camera is 2x. So, if you buy a 50mm lens, it's going to look like a 100mm lens on the BMPCC. So, you'll want to get something wider than you think you'll need; a 35mm prime would be good for portraits/interviews. If you want to do landscapes, you'll want at most a 12, and if you want to show real-estate interiors, you'll want an 8. If you film in 4K, but deliver in 2K, you can use the extra pixels to digitally zoom (or stabilize), so again, it's better to err on the side of wider rather than telephoto. Using a wider lens also has the added benefits of requiring less stabilization and having a larger focal plane, which translates to touching the lens less.
The price you pay for using a zoom lens is speed. Zoom lenses have more moving parts, and more elements than prime lenses, which translates into less efficient light transmission and a higher minimum f-number than you'd find in a prime lens at the same price-point. Yes, they are convenient. The cost of that convenience is image quality.
For my starter kit, I went with three ultra cheap manual lenses. I got a SLR MAGIC 8mm f4.0 for about a hundred bucks. It was designed for drone use, so it works perfectly on a gimbal, and even handheld, the footage doesn't look shaky. I wouldn't use anything higher than that without stabilization, though.
I also got a Meike 25mm f1.8, which translates into a 50mm equivalent, and is a good general-purpose lens. At 1.8, it works in low light situations, although it is not at its sharpest. It was also around a hundred bucks, so at that price, I'm not complaining.
Then to round out the kit, I found a m.zukio 40-100 olympus 5.6. I use this one the least because the crop factor makes it a 80-200 equivalent. It does have autofocus, though, and it was also VERY cheap. It's an OK lens for sports, in the daytime. At night, I had a hard time finding enough light with it at a local dirtbike track for HFR footage, and could just eek out a decent exposure at normal speed. I suspect a football or baseball field would have more light, though.
TO BE CLEAR, I don't use my personal lenses for paid work. These lenses are basically toys for practicing. For paid jobs, I rent good glass, and what I get depends on the shoot. If the shoot calls for a remote follow focus, I'll rent that, too.
