that's the hardest one for me too!

I don't do a grand barre, essentially because it's too difficult for me. IDeally you should strengthen your fingers so that you can, and truth be told it's much easier on an electric. But F is easier if you play it with your index finger holding down the 2 bottom strings on the first fret, the middle finger on the 2nd fret of the 3rd string from the bottom, and your index and pinky on the 3rd frets of the 4th and 5th strings from the bottom. The top string (6th from bottom) you don't play. This also makes an easy transition to C major, which I think is the chord pictured.

The nice thing about an F-chord is that you can move it up and down the neck just like a barre chord. So if you move from the first fret to the third then you have a G, or to the fifth fret and you have an A, etc.

What's a barre chord? The 6-string version with the index finger all across the entire first fret? The 4-string version shown is easy compared to that!

A barre chord is one that covers all the strings with your first finger. But I think the more important distinction is movable vs. open chords. Any chord that does not use any open strings can be moved up and down the fretboard. An F-chord is sounded xx3211 (that's the fret numbers for each string EADGBE), since it has no '0's then it's a movable chord.

makes sense. thanks!

This is one of the easiest chords to use your thumb with to get the full chord. Since the neck is so narrow at the first fret you can wrap your thumb around the top and catch the E string at the first fret. I know bad form, but it works great. I don't listen to those don't use your thumb people. Do what feels comfortable and what generates the best sound with full ringing on all strings.

I wouldn't suggest that. Why start bad habits you'll just have to unlearn later? It will kill you when you start playing more complex chords. Its best to use barre chords to get the low-E string. Rather than playing an F try an A, it's higher on the neck and much easier to finger. It would be 577455 (fret numbers for EADGBE).