As I've mentioned in the previous post, I'm no gear head (but if I had the cash then hell yea I would lol). But it is important to know your limitations, working with what you have and making the best of it as much as you possibly can. Even if you need to push the boundaries on post processing which will allow your gear limitations to expand. We'll discuss further on post processing in another post, but keep in mind I'm not a magician in post processing.
The following may mention some information based on the assumption you've mastered manual mode on your camera.
My choice of camera is a DSLR, more specifically canon, from T2i, XSi, 20D and a 6D. Now granted I did not expand much on my natural light photography until I had a 6D where it does have very high ISO ranges and great quality ISO up to 6400 and sometimes if really necessary 8000. This isn't a review of the canon 6D but just wanted to share my experience regarding ISO on the 6D.
The choice of camera will control most of your limitations of what you can and cannot do on natural light portrait work, and as mentioned control the size of available natural soft light during golden hours. Such as if your camera does not produce great or
decent quality ISO higher than 1600, your limitations will be much smaller than a camera like a canon 6D having decent quality ISO at 8000, so your window could be 30-60 minutes possibly.
You can choose any camera system, even a cell phone. As long as it has decent or great ISO ranges and doesn't produce too much noise you can recover some shadow or highlight details in post processing, especially phones with RAW files. But keep in mind cell phone's dynamic range is very limited, its no magic bullet where you can pull details from thin air without the data existing.
While cameras are a big deal to what you can do, a lens is as much if not more important because in my opinion shooting at open and fast apertures will not just bring in more light but as well blur/bokeh the background and help with lackluster compositions where you have little or no control of a composition so using bokeh heavily or lightly will assist with the composition of an image.
Types of lenses I recommend are FAST lenses, such as apertures ranging from f/1.2 to f/2.8. Granted most f/1.2 lenses out there are not in the budget of most photographers. Now I can't name specific ones outside of canon but if you do heavy research on your camera system ranges from prime (non-zoom lens) lenses you should have the option to purchase (or rent) a fast lens. A prime in my opinion should be your first choice in looking for a new lens for shooting pure natural light portraits, but they can be pricey even used ones. So there are options for zoom f/2.8 lenses which as well can be pricey unless you look into 3rd party like Tamron, Sigma, etc. lens manufactures.
A lens I highly recommend is the industry popular well known to being the best for all around portrait work is the 85mm lens. Either the 85mm 1.4 or 85mm 1.8. Not sure if this falls in your budget but they can range from $600+ used, such as for canon mounts, a sigma is my personal favorite, especially when they decide to release an ART version of it. As for 85mm 1.2 lenses out there it will take a ton of practice and acceptance in your hit ratio being low if you shoot at f/1.2, but I've seen some amazing shots taken with it at higher apertures like f/1.4 and higher. The 1.2 version can generally cost used for $1,400 and up as of this posting.
I do admit prime lenses can be pricey though so if you cannot afford them for whatever reason I recommend is a 70-200 2.8 lens. I have a used Tamron 70-200 2.8 (non-VC, image stabilization). I've been using mine for 3+ years and its my primary lens for natural light work, shooting at f/2.8 - f/3.5 at 200mm most of the time to really compress the subject and create some or a lot of bokeh to the background.
Your goal should be (as a beginner natural light portrait shooter) is to shoot long focal length with fast apertures, like a 70-200mm f/2.8 lens. Once you've mastered that then explore into wider focal lengths like for instance the new Sigma 20mm 1.4 ART lens, which I plan to play with when I rent it, hopefully sooner rather than later. But if you ever venture into wide focal length you must keep in mind the distortion, know it, use it to your advantage to your vision of the images created with wide focal length lenses.
The Tight Budget Options
Can't afford what I've recommended, no problem. I've personally learned on the canon 50mm 1.8, which at the time was brand new selling for $100 (in 2011). You can either get that slightly higher priced or a yongnuo version (3rd party) or an equivalent to your camera system. Usually these are priced lower than a 50mm 1.4 lens just cause the camera manufacture knows and understands people need to learn to shoot on fast apertures on a tight budget. Once people do learn it they will obviously and generally buy a more expensive version like 50mm 1.4.
Now if you're stuck with a kit lens for whatever budget reasons, you can either sell the kit lens and spend a little on a 50mm 1.8 (which trust me will do you much better than a kit zoom lens) or using the kit lens to the best to your abilities. Which is fairly simple, so keep these quick tips in mind... zoom all the way out and shoot at the smallest aperture number, so if you got a 16-55 3.5-5.6 Kit lens shoot at 55mm ALL THE TIME! If you got a higher ISO to compensate the light loss and going to 5.6, do it, raise that ISO. If you have another kit lens like I did with my Canon T2i had the 18-135mm 3.5-5.6 then even better as you zoom all the way out the more the background will be blurred out with some decent bokeh than the 55mm would.
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