Zoidberg says:
I have a classic guitar, an acoustic guitar. I have problems because I am slow when placing my 2nd finger in the 6th string and my 3rd finger in the 1st string, 'cause my 2nd one touches the 5th string.
I wouldn't worry about that at all. I play the G chord like that all the time... with my 2nd finger muting the 5th string. My guitar teacher actually recommended it since it has a slightly nicer voicing than the typical way of playing G (with the 1st finger freting the 5th string at the second fret.
And while you are playing G that way, if you can get your 3rd finger to fret both the 1st and 2nd strings at the 3rd fret, then you will be playing G5... and while you are doing that, if you move your 2nd finger to the 5th string, and mute the 6th and 4th strings, you are playing C5... moving between G5 and C5 is easy, and sounds nice.
I would add though, that classical guitars tend to have wider necks and more spacing to the strings... which can make classical fingerstyle playing easier, but tends to make chords harder. You might want to change to a regular steel string acoustic with a narrower neck and see if that doesn't make a big difference. It did for me.
In the end, finger strength is a big thing. When I first started I found many chords hard to pull off... but with daily practice I was able to master most any chord within a week or two.
Good luck!