A couple of points. An acoustic electric guitar with a slightly curved fret board makes bar chords easier. Second, get some really light strings to start with o.10 for bottom E. This means they bend a lot easier being thinner, but you will get less sound. If you're miked or playing with others, it's no problem.

On the chord changes: start by picking just two chords, then count 1,2,3,4 change, 2,3,4, change. Then when you are comfortable and your change is quick enough to stay with the beat, cut the beat down to 1, then change, 2 then change, 1 then change, 2 then change.

When you change, don't try to do it fast. Usually it is easier if you lay an anchoring finger. This is the finger that most easily finds the chord, and the you place the other fingers afterwards. You'll find your anchor finger can become very quick at finding the chord but the other fingers will be slower to start with. The trick is to make sure you focus on doing it ACCURATELY, not quickly. The speed will come with time. If you go for speed first, you train your fingers to make mistakes and your overall progress is slower. If you focus on accuracy, then your final speed will be much quicker and fluent.

If you are practicing F, it might be good to go from F to Bb. F Bb Gm C are a nice chord progression that will really bring on your bar chords (first three are bar chords).