I was talking to an aspiring writer a little bit ago who insisted he wasn't going to bother sending his book to agents or major publishers because it wasn't good enough.
That's self rejecting - don't do it!
Now, this doesn't mean you should send a sword and sorcery story to Analog or space opera to Beneath Ceaseless Skies.
It means you should accept that as writers we are often (not always, but often) the very worst judges of the quality of our own work and let editors do their job.
I've been writing for long enough that I can sort of tell which of my stories are really good and which are only good. But I can't be entirely sure, and you never know what an editor would like.
The only thing you lose by submitting to major publications first is a bit of time.
You can lose a lot by wasting your best stories on for the love markets because you have some idea that you have to start at the bottom or because you don't have faith in your own work...