Hiiii Sourav!!!! Below I have mentioned some of the best institutes for UPSE preparation:

• Shri Ram IAS.
• Elite IAS Academy.
• Classic IAS Academy.
• Direction Institute for IAS Examination.
• Bajirao and Reddy Institute.

Coming to the second part of your question, you can't appear for UPSE before graduating. So you will also be needing to concentrate on your graduation which will also help in your basic UPSE preparation and for more you should keep yourself updated with the current affairs. You should give maximum time to newspaper reading as it will increase the area of your knowledge, try to write essays on different topics and the Institute will polish your preparations. Good luck!!