Let's go over some considerations for different items/placements.
When it comes to foundation, I will actually apply from a center area and push out the sides... so like say on my right cheekbone and then expand it out to the jaw line and hair line and in towards the nose. Given how foundation typically applies, it's easier to start high and bring it lower, hence why I start on the cheekbone and will expand downward and towards the hairline.
I'm talking here about the powder that you may apply over your foundation. Really, this one doesn't matter so much as it's typically easy to move that loose powder around but I also typically start on the cheekbone and will expand in a similar fashion as the foundation.
On my eyelid, I generally start around the middle and will go towards each side. As I mentioned in another entry, I tend to use dabs when I apply the first layer. You can use your brush in a sweeping motion to move the powder around if need be. If you're using a cream eye shadow, this may be harder to move around. That's the general principle.
However, if I am applying some eye shadow specifically on the eyelid on the inner corner or the outer corner to create an accent, I will start at the corner as that's generally where I want to have the most emphasis.
At the crease of the eyelid, we typically want more intense at the outer corner and less intense towards the inner corner (if you want any eye shadow there at all). Depending on the color and the product, I may start building the crease at the outer corner, working my way in or from the middle of the crease and build it out.
If I'm applying some eye shadow at the brow bone, I'll start from the eyebrows and bring downwards as I want the brightness to be at the height of the eyes.
Ah, the eyeliner is an interesting tricky one. If I'm using a pencil, I will nearly always work from inner corner to outer corner as the tip will generally be sharper (and thus make a finer line) at the start of use. If I'm using any other product (liquid liner or gel liner), I will start at some place away from the inner corner... it might be anywhere from like a 1/4 out to past mid eye. I make that decision based on how much product there is on my brush. If there's a lot, I will start closer towards the outer corner as that's the corner that needs to have the thicker line (if you're doing an increasingly thicker line). The motion, though, will still be from outer corner to outer corner as that gives the look that I like.
For blush, I always start on the cheekbone and expand towards the hairline. The reason is quite simply that you typically want more on the cheekbone and have a feathering effect towards the hairline.
There are many ways that you can start the application. And, as usual, whatever works for you is what you should be doing. But, if you've been unsatisfied with some applications, consider starting from a different spot than what you normally do. If you're using tutorials, also pay attention to where they're starting first, realizing that this is what worked for them and could work for you... or not...