Betta are not community fish, and should be on their own, so I would forget Betta in a 60g tank. This non-compatibility is two -way...the Betta frequently takes a dislike to other fish, especially colourful species (I have seen a Betta eat a neon), but small tetra often become fin nippers when confined with sedate or long-fin fish.
Water parameters are essential to know. Some fish have very specific requirements. Your municipal water authority probably has a website with water data posted, check there. If you do get a store to test your water, always ask for numbers, regardless of the test. Without the number, we are only guessing.
Fish compatibility is something of a science in itself, involving water parameters, environment (the substrate and decor), filtration (water currents impact fish negatively or positively depending upon the species and the current), and of course natural inherent behaviours--but it is not insurmountable. Many fish are intolerant of certain other species for one or more of these reasons.
Byron.