I am using Gaussian for theoretical calculation and I have already use LANL2DZ and MHF28 successfully. I would like to know if you have any other basis set that you can suggest such that I can compare the results.
It depends which property you are studying. It depends on the system too. Anyway, a double-zeta basis set usually provides good geometries.
If you want to benchmark your basis for your system, you can carry out a calculation with a higher basis. Here you can find more basis than the standard basis of Gaussian (then you have to use the "gen" keyword):
https://www.basissetexchange.org/
You can use something like cc-pVTZ-pp to check if the results are converged or not. Of course, the absolute energy of the system is going to change a lot (and it is not a problem), but check if relative energies (if you are studying a chemical reaction), geometries, frequencies... are close to the ones that you already have.
Yes, depends on what you want to study. We use LANL2DZ for organometallic/catalytic systems and it works just fine and is used commonly by a huge number of groups, though others use e.g. ECP28MDF from Stuttgart (http://www.tc.uni-koeln.de/PP/clickpse.en.html).
I guess as long as the results are consistent with experimental findings (geometries, enthalpies for reactions (if known)) there's no need to move to different basis sets.