Yes for New games

You mean outside the trilogy, or ME2 and 3? And is that the answer for the first, second or both questions?

The yes was for the first and the new games the second

So there is a "canon" profile for Shepard then.

Both yes and no

There is a default appearance (Background & Profile as well) for Shepard that can carry through all three games. It is probably more uniform in the Legendary Edition since the CC is the same across the trilogy, unlike the separate versions. Each game *can* import a Customized Shepard, but the separate games will probably require tweaking whereas the LE is a bit better at maintaining any personalization. Usually best to check Appearance before jumping right in, just to make sure.

ME3 wasn't able to import my custom Shepard's appearance from the first two games because the hair color wasn't compatible, and I wasn't able to recreate him very accurately either even though the starting preset I sculpted him from was still the same. It was a little disappointing.

Legendary Edition has the same Character Build in all 3 games. Original versions have different ones, mostly each game improves upon the previous one.

As for base profile and quick start, as others said both yes and no. There is no canon Shepard. The Male appears in all 3 disc covers, but back in the day of ME1 and 2 most people, me including, preferred Female due to superior voice acting and romances. But then came 3, ruining most romances for Femshep - Jacob and Thane are deadends, and while Thane has some closure it's the saddest one. Kelly is both boring and a deadend in 3. Garrus is the fun one and arguably the best one overall.

And in the same time, MShep had some of the best romances: Tali is amazing, and even great in 2 but rivals Garrus in 3. Jack is... Meh, but it's still better than Jacob. Miranda plays a major role in 3 and based on your choice she might even die which makes it unique. You also got Steve, the same sex romance which is emotional and beautiful even if you're straight.

So to summarize: MShep is most likely the canon one, his base appearance was based upon an actual human model in real life, while FShep had basic NPC face. The default option is Soldier.

But I strongly recommend making new Shepards especially in Legendary edition.

There's quickstart, AND a "canon" Shepard. Quickstart already has a look and class, but "canon" includes everything already, from a name, to a background, face, and class.