Budget DSLR or Mirrorless Camera

The cameras you mention are all great value, to be sure. The Nikon 3xxx series and the Canon SL also have interfaces designed to be helpful to beginners; Sony, not so much. If rumors are true, there are photographers who have wandered off into their menus never to be hear from again.

The main disadvantage to going with a DSLR is the fact that the mirror is only a hindrance when shooting video. You can't use the viewfinder because the mirror is locked up and the autofocus is limited to contrast detection unless you get one of the newer Canons with dual pixel phase detection. All academic if you're just going to shoot stills. Also, you get a more compact camera body, but this becomes a moot point if you don't also use compact lenses. Speaking of compactness, if you want a truly pocketable interchangeable lens camera, you should consider the Olympus pen-epl series and the Panasonic GF series, too.

Perhaps the main point I should make, though, is that ILCs should not just be viewed in terms of the camera bodies, you're buying into a system here. I started with a Nikon myself, only to feel constrained by their DX lens lineup, and ended up switching to Fujfilm for their prime lenses. Now my Nikon gear sits unused. In retrospect, it would have been better to explore the lens options first, and then pick a camera for the lenses. Oh, and while digital cameras become obsolete quickly, lenses generally don't, so if you find a deal that has extra lenses, that's the one with the better resale value down the road.

Most extra lenses on ebay are junk. 1 good lens is better than 2 bad ones.

Between the types of cameras... DSLRs are generally easier to learn to take good photos on. Nikon and Canon have the best lens selections if you decide to add more lenses. The Sony's focus faster in video. The ergonomics of the DSLRs is generally better. The physical dimensions of the mirrorless tend to be smaller.

Among those DSLRs...
The Nikon's tend to get better reviews and with the same quality lens, the Nikon will produce an image which is less noisy and has more dynamic range. The Sony splits the difference between the Nikon and the Canon, being closer to the Nikon.

With the Canon lenses, to start with make sure the lenses have IS (canon for stabilization)
With the Nikon lenses, to start with make sure the lenses have VR (Nikon for stabilization)

I've owned all three brands. I still own a Sony and a Nikon. I prefer Nikon. I use Panasonic and Sony for most video, Nikon for everything else.

The Canon you're looking at does not have dual-phase detection and has the slowest AF of the bodies you are talking about.

The comment about limited DX lenses for the Nikon is poppycock. Nikon has the largest lens collection (followed closely by Canon). The DX bodies can shoot FX lenses just fine.

The worst UI is in the Olympus cameras, you're not considering one but Schwebbz mentioned them.

I didn't mean to suggest the Nikon lens lineup is bad, it's in fact second to none in almost every regard. Prime lenses for dx is the one exception; if you want to use zooms primarily, or you're thinking you might switch to fx at some point, you'll be spoiled for choice.

Your statement on DX lack of primes remains false.

When I had a DX, I owned (at various times) 11 primes I used on DX (20mm, 24mm, 35mm 50mm, 85mm, 90mm, 100mm, 105mm, 150mm, 180mm, 300mm). I very briefly owned a 10.5mm and 28mm as well, but didn't keep them (took them in trade and sold them). I didn't even own 10% of the available primes. What prime lens for DX are you implying is missing? It is FUD to refer to the DX prime lenses and exclude the FX lenses which work just fine on the DX line up.
What is the difference between the DX only 35mm f/1.8g and a FX 35mm f/1.4g? When mounted on a DX body the only functional difference is the f/1.4 is around 2/3 of a stop faster but that is a function of the aperture not the FX vs DX. The DX line up had something over a dozen prime lenses (more now) in the 45-60 range alone. I think there may be close to a dozen under 35mm as well. Over a dozen primes over 200mm. No line has more primes than the Nikon DX lineup, not even the FX lineup since there are a couple of primes which are DX only (unless you use the Nikon FX in crop mode). A DX body can't tell if a lens is DX or FX because it doesn't matter.

There are primes ranging from 6mm to 1200mm and most every conceivable length in-between. Even if you exclude the rare primes, your DX range remains 10.5mm to 800mm.

Shoot what you like for whatever reason you like, but don't fabricate facts to justify it.

sure, if you're fine with paying more money and carrying bigger and heavier lenses with more glass than you can make use of, you can use fx lenses on dx bodies, no problem. That proposition doesn't appeal to me, though, and I know I'm not the only one.

As far as I can see, there's currently four prime nikkor dx lenses listed on nikons website:
AF-S DX NIKKOR 35mm f/1.8G
AF-S DX Micro NIKKOR 40mm f/2.8G
AF-S DX Micro NIKKOR 85mm f/3.5G ED VR
AF DX Fisheye-Nikkor 10.5mm f/2.8G ED

of course, it's not as bad as all that, there are a number of third party options, and there's fx if you're willing to go that route, but it's not FUD. Anyway, we're getting completely sidetracked here, the point I was making is that lenses, flashes and other accessories are important parts of the whole you ought to consider when buying a system camera.

More BS. Most certainly FUD. You are clearly attempting to mislead and misinform. You can keep repeating your nonsense, but repetition won't make them true.

The Nikon 50mm f/1.8g is a "FX" lens, meaning it works equally well on both FX and DX. It weighs less than the SLOWER Fujifilm 50mm f/2 (200g vs 185g). Fuji doesn't have an 85mm, the closest is the 90mm and is also only f/2 but weighs a staggering 540g compared to the 85mm f/1.8g (an FX lens) which weighs only 350grams. Who is it that is lugging around the over-weight lenses?

As for the third party lenses. Nikon and Canon do enjoy the best 3rd party support by a country mile. I'd would not be surprised if both have more high quality 3rd party lenses to chose between than any 3rd mount has lenses in total. I have two other mounts (Sony and M4/3) and buying stuff for the Nikons is a ridiculous exercise of 'so many choices'... compared to the other mounts. It was the same for Canon back when I shot Canon.

There are larger heavier options. My old 50mm f/1.4d weighs 230g. (I keep it around because it has a manual aperture in case I want to reverse it). My newer 50mm f/1.4g is 280g. There are many other 50's alone to chose from. Their weight varies, again options not requirements.

This is relevant because you inserted this nonsense in the conversation as a minus for DX when the OP is considering DX, Canon APS-C and Sony. Falsehoods and distortions about one of the mounts is clearly not called for.

Guys....we've gone far beyond " a cheap beginner camera" "used from ebay"

I see exactly where both of you are coming from, but let's rein in the minutiae.

Megapixels only really matter if you're printing images onto very large canvases where DPI comes into play; advertising billboards for example.

The most important factor in a camera is how it feels in your hands. You don't want to miss a shot because you're navigating a complicated button layout or menu. I shoot with a Nikon D90, which is almost a decade old, for this exact reason.

The second most important factor is that when you buy a camera with interchangeable lenses, you're actually buying into an ecosystem, so you need to consider what lenses and accessories are available for your chosen brand. It can be very expensive to switch from one brand to another.

The best thing you can do is go out and try the cameras that interest you.

A budget DSLR well my Canon 450D (£130 used with 50mm kit lens) was a great starter camera and i took some amazing pictures with it. I still use it even if i have a 650D now.

The megapixel count matters, but less than skill. Like bicycle_repair_man I shot with a d90 for a while. Before that I shot with a Canon 15mp, I got plenty of good photos with it too. When I upgraded from the d90, I did so to another 12mp (d700). I then bought a d750 when they were released. The 24mp d750 takes better photos than my older cameras in most ways (better dynamic range, lower noise, and more image detail). But a good photographer with a 10-12 mp camera can take better photos than a beginner with a 36-50mp camera.

megapixel count...

For the OP, without clicking on the spoiler below, guess the 'megapixel' of the camera that took this:



In the right hands, $500 worth of equipment can end up in an art gallery
In the wrong hands, $20,000 worth of equipment will turn out crap pics.

Some of the images I sold the most of were from a 3.3mp camera. But that doesn't change the fact that my images from my 24mp are better than from my 12mp, and part of the reason is the megapixels. Also in your 15 to 20 comment above you are ignoring what happens in each jump in MP. The other aspects of the sensor improve. Lower ISO noise, better dynamic range and yes better image detail.
MP is not the end all do-all. There are plenty of horrid point and shoot cameras with lots of pixels and no image quality. I was only talking about DSLR and Mirrorless cameras (assumption being m2/3 or larger).

Right.
But far too many people focus on the megapixel number, as the defining and most important factor.

I prefer the d5200. It has a better menu system and a more advanced focus system.