Welcome to Guitar Tricks! When I was first learning guitar, I was convinced that whoever invented the F chord was evil. That is to say, EVERYone has trouble with that chord in the beginning.
I don't think a different guitar is necessarily going to be the magic bullet you're looking for. The classical guitar's nylon strings are easier on beginner fingers than steel strings. True, the neck is wider and the strings are further apart, but it sounds to me like your trouble has more to do with hand angle and strength, rather than the type of guitar you are using.
When I teach beginners, I sometimes recommend using an F Major 7th chord in lieu of an F Major chord, while you are still in the process of developing your skills and strength. The F Major 7th chord is all the notes of the F chord, with one exception: you leave the high E string open. In other words (?), it is fingered as: XX3210. In other words, no double-duty for your index finger.
For now.
Keep it as a goal on your list to conquer the true F major chord as your skills get stronger.
If you want some resources for nurturing your hand strength and proper angle, you might want to check out the Spider Legs Warm-Ups. They are aimed at developing those exact skills.
Here's the link:
”SPIDER LEGS” WARM-UP EXERCISES
http://www.guitartricks.com/tutorial.php?input=621
Keep us posted - and have fun!
Best wishes, Lisa
Lisa McCormick, GT Instructor
Acoustic, Folk, Pop, Blues
Full Catalog of Lisa's Guitar Tricks Tutorials
Find Lisa on Facebook!
Acoustic, Folk, Pop, Blues
Full Catalog of Lisa's Guitar Tricks Tutorials
Find Lisa on Facebook!