Best Of

I agree with Ziggy on lens choices, but would also consider:

Nikon 14-24mm f/2.8G (possibly the best lens ever)
Tamron 17-50mm f/2.8 XR Di-II LD
Sigma 24-35mm f/2 DG

For the 50-100 range, Sigma has a new 1.8 that would be worth considering.

I would also highly recommend that you consider lighting equipment. As Ziggy mentioned relying on the sun/weather is going to be limiting.

No problem. Remember, I'm not saying that a zoom couldn't do what you need it to do. Lots of shooters have been successfully using a 70-200 zoom for portraiture, or something like it. Zooms can be real money savers, even the expensive ones, in the long run for their multiple uses. Just keep in mind the pros and cons of lens IQ (read: picture quality) when considering a do-all zoom - because many of those can't really do all, at least really well.

I had an old Tamron mid range zoom, now since sold off, that had really good, but not great, bokeh for backgrounds. It also sucked for true wide or tele, but it was relatively cheap and sharp. While I'd love to always push Dgrin for threads that answer questions like these, I'd also look into POTN (Photography On The Net) for specific Nikon lens examples. Those threads are very long and offer hundreds of example photos from forum members. There are many more Canon shooters there than Nikonians, but going through the many threads could very well steer you towards a better purchase decision. Look at background bokeh specifically, and do a shooting post mortem in your head of the subject, how far away they were, the EXIF info and f-stop used, the background image quality, and all aspects of how they're shooting their subjects.

There's a thread here that asks members to post their bokeh or soft backgrounds... https://dgrin.com/discussion/257956/post-your-bokeh-or-soft-backgrounds/p1
I don't want to pick on any individuals, but some of the "soft backgrounds" are just horrible. If a portrait was taken with whatever they're shooting with, I wouldn't at all be pleased with the results if a photographer was handing me those if I was a paying client. Others are just beautiful. You'll see the differences fairly immediately just going through there.

While there are opportunities for beach portraiture, limiting yourself to "... natural light doing beach portraits" is going to be extremely limited opportunity indeed. Finding that perfect compliment of site plus background and a suitable available light is just not going to converge on a regular basis.

Most of the time you will either have strong but contrasty lighting when the sun is out, or dull and lifeless lighting when the sun is hidden behind clouds. Reflected fill can work with the strong-contrasty light, but then you would also need a skilled assistant to help with the reflectors and you'll get more partially closed eyes. And light that works for the background of the scene may not be suitable for the subject matter.

Small, external "speedlights", are tremendously useful outdoors for both conditions of strong, contrasty ambient light, where they are useful as fill light, as well as overcast days where speedlights can be used for both key and fill light. In a backlit scenario, with a setting sun behind the subject for instance, speedlights can again provide both key and fill for the subject.

Getting back to lenses, I use different lens focal lengths for different portrait needs.

For instance, on a DX body like the Nikon D3300 or D7100 that you mentioned, I suggest a telephoto lens of at least 50mm to as much as 200mm for a head shot or head-and-shoulders. (So a 75mm - 300mm, full-frame-135 format equivalence.)

For a 3/4 length and full length portrait I suggest 28mm to 50mm actual focal length. (So from a standard/normal focal length to a short-telephoto.)

For an environmental portrait, which includes a lot of the scenery or even much of the scenery as in a vista landscape portrait, a wide lens from 10mm to 24mm might be suitable.

I use a combination of Nikon D7200 and D7100 as my Nikon DX bodies, and my choice of lenses for an outdoor portrait shoot (of what I currently own) would include:

Sigma 50-150mm, f2.8II, APO HSM, for the tighter shots. This is suitable for both head shot or head-and-shoulders plus 3/4 length and full length portrait.
Sigma DC 17-50mm, f2.8, EX OS HSM, suitable for 3/4 length and full length portrait plus some environmental portraits. Also works for small groups.
Tokina SD 12-24mm, f4, IF DX AT-X Pro, suitable for the environmental portraits and larger group portraits.

Note that of the above lenses only the first two lenses, the Sigma tele-zoom and the Sigma standard/normal zoom, are fully compatible with your existing D3300, because the Tokina super-wide zoom is a "D" type lens and requires an in-body AF motor like that in the D7000-series bodies.

Yes, I also have prime lenses but I try not to change lenses too much outdoors to prevent dust/dirt/grit and pollen problems with the image sensors.

Of the above lenses, the Sigma DC 17-50mm, f2.8, EX OS HSM is a truly professional joy to use, with wonderful sharpness and contrast, sharper than the Nikkor DX 17-55mm, f2.8 (IMO) and the optical image stabilization allows capture in lower light without a tripod. It is slightly faster to focus and focus accuracy also seems better on the D7200 vs the D7100, but still acceptable on the D7100.

The Sigma 50-150mm, f2.8II, APO HSM has more difficulty acquiring focus, in my experience, leading to more OOF rejected images, but still usable. No longer available new, it still pops up in the used markets fairly frequently.

I honestly haven't used the Tokina 12-24mm, f4 for people stuff as I normally use a Canon FF system for portraiture (although now fully retired so only family/friends.) Still, it seems perfectly capable if only a little slower than the Sigmas.