Thanks for all the replies. Birthday is coming up and I always buy myself something for it and a DSLR or mirrorless was on my list. All the information provided has helped greatly, thanks again!
I got a Sony NEX 6 when it came out, followed by an a6000 when they went on sale during a holiday season. I couldn't be happier with both cameras, so I'd certainly recommend the a6300 that you mentioned in your OP. Actually, given what you've said, I'd recommend the a6000. Sony still sells it, and it's a lot cheaper than the a6300. If you eventually outgrow it (and I haven't come close to doing so), you can buy the a6300, a6500, a6700, a6900, or whatever model they're up to by then. The lenses you buy now will work on future models, and I suspect you'd want to keep your a6000 as a backup.
To add my two cents' worth to the discussion, I started with a 35mm SLR in the 1980s, got a 3MP Nikon 995 digital camera in 2001, and upgraded to an 8MP Canon Powershot in 2004. When I got an iPhone 4 in 2010, I was amazed by the camera's quality. At that point in my life, I was no longer seriously into photography, and I wondered whether I could get by with just an iPhone. I got one of those Olloclip three-lens kits. They were pretty cool, but it was a pain having to remove my iPhone's case every time I wanted to use the lenses. Then when I upgraded to the iPhone 5, which had a different form factor, the Olloclip lenses no longer fit. That's something to keep in mind when buying accessories for phones and tablets.
In 2013, I started following some photographers' blogs, and that inspired me to get back into more serious hobby photography. I was leaning toward a Nikon D7100, but after reading positive reviews of the NEX 6, and playing with both the D7100 and NEX 6 at Best Buy, I decided that the Sony's smaller size and lower weight offset the Nikon's few technical superiorities. I remembered my years of lugging around my SLR and lenses in a backpack, and I didn't want to return to those years.
These days, I always have my iPhone 6S Plus with me, and I use its camera all the time. But when I travel or otherwise go out explicitly to "take pictures," I use my a6000 and whichever lens(es) are appropriate for the situation: the 16-50 kit zoom, the 55-210 zoom, the 35 prime, and the macro (all native Sony e-mounts). At home, I keep the 35 on the camera, because it's great for getting those low-light indoor shots of our pets doing cute things. Outdoors, the 16-50 does most of what I want. (No, it's not the greatest lens ever made, but neither is it the piece of crap that some people say it is.) The 55-210 is great for wildlife photography when I can't get close to the wildlife in question. That's one thing you can't do with a phone camera: extreme optical zoom. I bought the macro for food photography, when I was thinking of starting a food blog. I didn't start a food blog, but I use the macro occasionally.
My 27-year-old stepson had been posting really nice iPhone photos on his Facebook page. It was apparent he had "the eye." He started accompanying a couple of pro-photographer friends on photo shoots. I recently decided to give him my NEX 6. He was thrilled, and he's been learning all the camera's features, experimenting with manual mode, and putting great thought into his compositions. I'm thrilled that he's thrilled.
Maybe there will come a time when smartphone cameras will be good enough for what I do, and when software algorithms will compensate for the limitations of optical physics. If you like experimenting with depth of field, there's only so much you can do with a phone camera. Anyway, good luck with whichever camera you choose!
