If budget is a constraint then servicing will be a better option since the 760D is still a relatively new and capable camera.
Assuming class B service (more than 40 mins) plus a shutter assembly replacement, it shouldn't amount to over $500 at canon's service center. I had a 7D mark II shutter replaced a while ago for around $400 there. You can find the
pricelist for servicing here, any parts replaced will be additional cost (even if under warranty).
However, if cost isn't an issue and you have already invested in Canon's lens system, a newer camera would be something you can consider. I personally recommend the 800D among the other DSLRs, which offers most of what the the other canon models offer. If you want to go for a camera that has a familiar layout as the 760D, the 77D or 80D is a good choice too.
It is also a common misconception that shutter count does not matter on mirrorless cameras (i suppose you meant EF-M, EF-S is canon's crop sensor DSLR lens mount). Those mirrorless cameras do still have mechanical shutters! That being said, these shutters generally last longer than similarly priced DSLRs (I suppose because no mirror? I'm no expert at the science behind why this is so >.<). You can consider Canon's M5 or M6 if that is the case, though all your current canon lenses will require an adapter to be used on the mirrorless canons. Alternatively, sony's a6000/6300/6500 or fujifilm's X-T20 are also good choices if you want to switch brands!
Lastly but not least, regarding where to buy, I buy my cameras from Cathay Photo because they are the most reliable and I've been buying from them for years, but you can also buy from Canon's website or IT shows (because you can potentially get a better deal + more freebies). I recommend you take a look around and maybe ask for a quote from local photography stores such as
alan photo,
cathay photo,
ms colour,
tk foto and see which of them give the best price lor haha.
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Edit: Also saw the 6D reply
By most means, the 6D mark II is a very capable camera, though it is definitely pricier than most other options. It should also be noted that while you get a larger sensor, the AF points are quite clustered in the center and hence, not the best pick if your daughter shoots action or anything that requires consistent autofocus tracking. You may also need to buy new lenses if you do not have any EF (full frame) lenses currently and they will most definitely cost more $ than EF-S or EF-M lenses as you can't use those on the 6D. As a result, the camera may be heavier and larger.
Personally, I use a few of canon's crop series cameras (700D, 70D, 7D II) and a 5D II, and if you ask me I would say the crop series cameras are good enough that the additional cost of the 6D is somewhat unwarranted (to me at least) since the things that I shoot don't require what the 6D offers more than the cameras I already have. If your daughter frequently shoots in low light situations or fashion, the 6D would be a better choice.
