A proper setup (especially action at the nut) goes a long way, as do lighter strings (11s instead of 12s or 13s). My recommendation is to either learn to setup your guitar yourself (it really isn't hard) or get a good tech to do it.
Couple of tips for a good setup:
The neck should almost be straight. Press the Low E at the first fret (use a capo) and at the last fret ( or where the neck meets the body). Now check at the 7th fret, there should be just a little distance between fret and string. If the strings buzz at the first fret the neck is too straight, back off the truss rod a little.
Press a string at the 3rd fret. Again, there should be very little distance between the string and the first fret now. If not, you need to file the nut slots a little deeper. This will also help with intonation on the first few frets, since it will be sharp if the slots aren't cut deep enough.
Measure the distance from the 12th fret to the (unpressed) low E string. I prefer around 2.5mm for the low E and 2mm for the high E.
If it is too high, you need to take the saddle out and sand it down a little. Just some 400 grit sandpaper on a flat surface will do.
Another important thing is the proper technique.
Check out justinguitars video on the F-chord if you haven't:
https://www.justinguitar.com/guitar-...f-chord-bc-161