Something like a nationalised bank will help your cause since their lending rates are way below what private banks have on offer.
To quote an example, for a loan under 20 lakhs, someone like HDFC will quote about 11.75% currently, whilst Bank of Baroda will quote a max of about 10.50%. Processing charges are lesser for the latter too.
The trade off would be that for a nationalised bank, the santion time will be more, typically under a month or something.
Do PM me for more info if you have any doubts. I have tried doing a fair bit of research on this of late.
All the best