I learned to play barre chords by playing "power chords" or just the three bottom notes.

You can fake F for a bit by just playing the "power chord" F as 133xxx. Use your index to play the F on bottom, and your ring and pinkie to play the C & F (the "3 3" part.) Mute the 1, 2 and 3 strings as best you can.

After you get used to that, you can start putting your index finger across all the strings and add your middle finger to the 3rd string for 133211 - which makes a barred F. This gives you a big fat sounding F chord.

Still in F - if you lift the middle finger for 133111 you get F minor.

Once you've learned that trick, the whole guitar neck starts opening up, moving the F pattern up two frets give you G, and so on.

From there you just keep learning.

Good luck,
Neil