Mechanical Engineering

No, at this rank, you will not get government college for lateral entry.

Every field has its own merits and demerits. The difficulty level depends solely on the student's determination and interest towards the subject. However, answering your question, mechanical engineering is felt by most people as slightly more difficult when compared to civil. You have to be good at maths for both fields but mechanical demands more skill and knowledge about gadgets.
All the best! I would really suggest mechanical engineering. Please upvote my answer if it is helpful.

Hello, hope you are doing well.
All the government colleges of the home state are good for mechanical engineering.
You will definitely get a government college with 65000 rank along with your mechanical branch.
Google the best government college of your state and get the best one by going through the counselling.
All the best.

Hello Shourey,
Frankly speaking, your rank is a little bit on the lower side. However, to help you, I am attaching a link that will predict colleges for you-
https://www.shiksha.com/b-tech/resources/ts-eamcet-college-predictor

Hello, hope you are doing well.
The fee structure for MS Ramaiah Institute is two lacs per annum for all engineering courses, as per 2017 records. The hostel fee is seventy thousand for college campus hostel and food. Other fees including university charges per year are 20 thousand including bus and library.

GRIET takes admissions on the basis of EAMCET, (Engineering, Agricultural and Medical Common Entrance Test) exam conducted by Government of Telangana. Moreover, for the cutoffs for this, kindly follow the link:
http://www.griet.ac.in/eamcet.html

Both branches are equally important and good. It depend on your interest. Moreover, if still you have to choose keeping in mind your aim to prepare for the civil services exam, I would suggest you to go for mechanical as a backup option.

The University of Melbourne
The University of Sydney
The University of New South Wales
Monash University
The Australian National University
RMIT University
The University of Queensland University of Technology (QUT)
The University of Adelaide
The University of Western Australia

Frankly, you need 102 marks for OBC to get into NIT - Pondicherry to get into the 5-year integrated course for mechanical and around 115 for the 4-year course.
Moreover, kindly mention if you want to know about a specific college.