Hmmmm how resistant is the screen to scratching? I've never used screen protectors, but the system I just got had a loose screen protector that's still good to use hanging in the box.
I've always avoided using them since every time I've tried I end up applying them incorrectly and end up with tons of bubbles and dust trapped underneath. I'm usually pretty gentle with my handhelds.
Not sure about the natural screen's resistance to scratches; I never take that chance.
In my opinion (and I'm pretty picky about my screens always being pristine), the official Sony protectors are AMAZING. I got the starter kit which contains two of them and they're really high quality, on par with the Realook ones you can buy for smartphones (which I also consider the very best in that arena). There's literally no discernable evidence that it's on, aside from where you can see the edge. (See below).
As far as putting them on, I used to have that problem but I've finally perfected it..this is what I do. First, clean the screen thoroughly, preferably with an alchohol-based screen wipe, then dry it off with your microfiber cloth.
Turn your shower on hot and wait until the bathroom is super steamy. Go inside and close the door, and wait about 30 seconds then turn off the shower. Pull out your Vita and the screen should get some condensation on it right away..just wait until the condensation clears off naturally (don't wipe it while it's wet), then check to see if there's any bits of dust or anything on the screen. There shouldn't be due to the steam, but if there is just lightly dust it off. The Sony screens have a nice guide layer so it's easy to place them on properly; just follow the directions and you're good to go. There may be a few big bubbles, but there shouldn't be any hairs or dust particles, and it's really easy to wipe the bubbles out 100% by just gently pushing them towards the edge with your microfiber cloth.
A bit long winded but this method works for me every time, I've done it now about 7 times in a row without a SINGLE blemish on the screen when its all said and done.
Here's a picture of my Vita with the official Sony protector on..you can clearly see the edges of the protector but there's no dust or bubbles, it looks really nice.