While playing basic Chords like A, D , E etc. my finger-tip touches the adjacent string and thereby the note tone is ruined. So my question is should I continue playing and practicing chords or I should switch over to playing simple children melody of one or two verses or should I switch over to practicing exercises relevant or prescribed for such problem ? I have just started learning guitar for last 15 days. So please guide me in the beginning of my guitar learning path, so there would be a solid and proper foundation.
Since the guitar is one of only a few instruments on which chords can be played, it's important to be able to play chords!
If you are touching other strings, be very careful pressing down - obviously. Part of your practice regime now should be slowly placing fingertips on strings, pressing down, and checking each string in turn, to hear 5/5 or 6/6.
If your fingers are quite wide, there's an option of using one finger for two strings, which works well for both E and A. On E, your middle finger is probably wide enough to cover strings 5 and 4 (the A and D strings). With open D, you can experiment with different fingerings - there are 12 available. There should be a couple which work for you. Don't always go for the fingering a book or website (or even some teachers) tell you to use. Work out what's best for you.
And play all sorts of things, melodies, riffs, chords are only a start.
Just keep at it. This happens at the beginning. Your fingers will get stronger and more adept at fingering the chords cleanly. Two things you can practice are smoothly switching between chords and fingering them cleanly and you can practice both at the same time by just going very slowly and deliberately placing the fingers in the correct place.
If you absolutely can't get them to sound cleanly just keep at it. You'll get there.
First, are you taking lessons? Do you have a mentor that can view your hand posture and correct it? A better question might be how do I fix this problem, rather than should I continue.
Practicing "children melodies" will not make chords easier. If you're 15 days into it you may not have the coordination to play chords very well. This takes time and practice, and a teacher would help.
You need to make sure you are fingering the chord properly, and before that that you are holding the guitar properly (bad hand posture will create more opportunities for problems). Then make sure you CAN play the chord without ruining the sound (some cross string touching may not be a bad thing, we do this to create dead strings in chord forms that skip strings). If you can get get it right once, you can get it right every time. You just need regular practice forming the chord, playing, then releasing the hand and reforming the chord. Make sure you are not squeezing the neck too much (or at all for that matter). Once you can get a chord reliably start transitioning from one to the other, perhaps based on a song with a simple chord pattern.
Finally, there are alternate fingerings for many chords and you may want to look into that. A good guitar teacher would be familiar with them and be able to give advice based on watching you play.