The most obvious answer is the one you have with you when you take a photo. But I’m going to assume the interest goes beyond just snapping selfies with friends – any smartphone is good, (D)SLR camera is actually awkward and bulky for selfies. I know, I tried. DSLR, however, is good for images like this:
Brand is not important, so I will not throw around any brand names. I started my semi-professional photography with Soviet-era cameras, switched to digital going through Kodak, Minolta, Fuji then finally arriving at Nikon after extensively testing Canon. I loved Canon’s usability and handling, it’s just Nikon’s images look better to me personally. So go and pick your own toys. All cameras these days take amazing images – technically speaking. It’s not the hardware that matters.
What is important in taking photographs of people is how you use the camera you have and how you compose (or frame) the shot. Trust me, I’ve seen people with $6000 cameras and $12000 lens not knowing what they do. I’ve worked with a gentleman who used 10 years old flash, gaffers tape and pieces of a cardboard to stage a fashion photo shoot outside in direct sunlight with clouds swinging in and out due to high wind. The resulting shot looks like it was taken in the studio.
If you are just starting you may not know which “people” photography you want to do. It could be portraits/headshots, could be fashion/editorial or it could be action – like sports or street photography or recreational activities. In most cases you can start off with one or two lens and when you figure out where your passion lies – you can start investing in a more specialized equipment.
My personal favorite is any of the vibration reduction basic zoom lens. You need to cover range between 35 and 135 mm when using standard 35 mm frame – called FX or full frame in digital photography. Consumer-grade cameras usually have smaller size sensors so you need to adjust lens’ native focal length to sensor size.
As a rule a 50 mm is considered “human eye” perspective. Portraits mostly shot at 80 – 85 mm. Depending on how far from the subject you are positioned – a longer range can be used. Personally I prefer to use my 70–200 mm for portrait, beauty and glamour and boudoir photography, but I constantly run into issues if I have to shoot in small spaces. In those cases I fall back to Nikon 24–120 mm. Yes, it distorts images differently but if you apply proper correction in Camera Raw or Lightroom (whichever one you’re using) – it shouldn’t be an issue. One nice feature of 70–200 mm is the aperture of f/2.8 which blurs background nicely. It’s a big “YES” for beauty or fashion but I’d say it’s a “NO” for street photography.
For anything involving fast movement (sports, street) you want to use fast lens and probably could invest in the camera that supports less noise on high ISO settings. Depending on your budget it could be something semi-professional or completely high-scale. I’d suggest studying DPReview’s extensive camera knowledge base before making a decision here. For me it’s always a compromise between budget and camera’s capabilities. For example – this photo of a martial arts athlete still came out somewhat blurry at his feet even when I used fast shutter – it wasn’t fast enough.
I haven’t done a real street photography for a while, so I can’t really say what you may want to do there. Again – do you want to focus on a specific person, emotion or face, or do you want to capture the street, the location with people interacting? Based on that I’d say the same basic 35 – 135 mm range is enough to get started and figure things out. The closest I got to shooting street photography was obviously staged “Love Story Gone Wrong” but I still ended up pushing my equipment to its limits (I give a better account on that in my other blog post: How To Learn Night Photography?)
To conclude (TL;DR): pick any camera you can afford, start with lens that cover most shooting scenarios and work your way through specific topic that you are passionate about.