1. Substances that are coloured will absorb part of the electromagnetic spectrum and reflect another.
Non-transition metal solutions tend to be colourless suggesting they absorb no part of the spectrum.
2. Compounds that are coloured have electrons promoted from a ground state to an excited state. This energy transition must coincide with the frequency of light absorbed.
For Na+ to excite electrons they must be promoted from their outer 2p orbital to a 3s orbital. This energy gap is too big.
3. In the case of Ti(H2O)63+ ions there is a narrow gap in electron energy levels which matches the energy inpart of the visible spectrum.
This electron is not promoted to 4s since the gap is too large. Instead the presence of the water ligands causes the energy symmetry of the 5 '3d' orbitals to distort and split into two levels.
The new energy gap matches part of the visible frequency (green/yellow) therefore the resulting solution appears purple.
The principle is the same in other systems but details more complicated since there are more electrons involved.
Different ligands affect the energetic symmetry of 'd' orbitals differently therefore, producing different colours.
Different oxidation states will vary colour greatly due to different numbers of 'd' electrons available.