I think this depends on your purpose. if you just want to confirm the structure during the Synthesis procedure or to check the purity, the 1H-NMR is enough due to very Little compound needed and fast . if you dont know the structure and want to charaterize it, the both 1HNMR and 13CNMR are needed.
If the compound you are talking about is already known, and your aim is only to compare with available spectral data, then a simple 1H NMR spectrum is sufficient. It is easy and quick to acquire. Depending on your sample, something as little as a 10mg is sufficient for a decent spectrum. If you are characterizing a brand new compound (or say a derivative) then you will need all the possible data you can acquire. A good 1H NMR spectrum, a 13C (proton decoupled) plus a suite of 2D techniques will help establish the framework of your complex. Depends on the facility you have at BITS. 13C (because of low sensitivity) will require more time to record a decent spectrum and at least 75-100mg compound. Take all of these into consideration.
Like Bo has pointed out, purity is essential. Do not waste your time running a 13C spectrum if your 1H NMR spectrum is not clean.