Check your nut.
First of all, fret the guitar at fret 3. How much clearance is between the strings and fret 1? They should be just about touching.
If they are touching: Your nut slots are too low. You can shim the nut. Start with a little strip of your string envelope, put it in the slot, and coat it with superglue. Then put the nut back in. Repeat as necessary.
If they are more than .010 off:You could lower the nut or you could make the nut slots deeper. You need special files to do the slots, but all you need is sandpaper and a flat surface to do the whole nut. Do a little at a time.
To get the nut off, loosen the strings. Push them off to the side of the fretboard (3 one way, 3 the other) and pry gently with a small screw driver. It should pop off. You'll go through a set of strings with all your loosening and tuning back to pitch. It's pretty hard on the strings.
Check Relief
Press down at fret the guitar at 1 and 12. Look to see how much space is between the strings and the frets around frets 7,8, 9. Should be a little bit of space there. No more than a credit card, I prefer mine about .010 (string size). If there's a credit card or more, give the truss rod 1/8 turn tighter, wait a few minutes and check again.
If after all this, you are still getting buzzing or fretting out and your action is 2mm or greater at fret 12, you probably need to consider a fret leveling. But do this other stuff first.
In the meantime, give some more information about fret buzz. Where? All frets? Only frets above 12? Does it buzz on all strings? Does the buzz amplify? (some rattle on the strings is OK, you jsut don't want it to amplify.) Do you fret out on bends? If so which strings?
With a tuneomatic bridge you can't really do this, but if you have individual saddles, you can run your action a hair higher on the E and A strings, since they tend to buzz when you dig in (and are harder to fret cleanly up on the neck, for me at least). You can tweak it to your liking. There is no set rule, although following the radius of the fretboard is common.
The easiest way to set action is with a nickel. I use a nickel and fret #15. You can slide the nickel under the string and strike the string. When it just barely vibrates and rubs the nickel, you are good to go. Do that on every string and your strings will mimic the radius of your fretboard.