Shri G. S. Institute of Technology and Science

WIth the home state quota, you'll easily get EEE branch or at max ECE branch. If you are from outside MP, you'll then get civil or EEE.
STATS: Last year cutoff. Best of luck.

You need to clear JEE Mains with the valid cutoff to be able to stand for a seat in GSITS. Kindly go below the link to know the cutoff.
https://ask.shiksha.com/what-is-the-cut-off-rank-home-state-quota-for-general-category-candidates-in-sgsits-qna-4105847
Now, you need to go through few rounds of JOSAA counselling similar to that of NIT's and IIT's and fill your desired choice. As you freeze your branch, you need to go for on campus verification and then you are admitted into the institute after few days of processing.

SGSITS Indore is not a private and government institute but is state government. Funded, supported but run by administered and maintained by private organisation. These colleges are called autonomous institutions which runs on both private and government interference.

At least you need a ranking of under 35000 with home state quota to be able to get into GSITS. Moreover, you can get CSE at 21000 - 22000 rank and the least IP at 35000-38000 closing rank.

Sorry, as with home state and your category, you need atleast 120 marks to be able to get into it this year which though your rank will not satisfy. I would suggest you to move for college level counselling after JOSAA counselling which may lend you something better.

With your marks, you'll not be able to get into GSITS with any of the branches as minimum you need is 145 with IP branch to get into it. You can only try in college level counselling which occurs to fill the vacant seats after JOSAA.

The best government college you will get is RGPV Bhopal with this. Also, you have a better percentage, hence, you also have chances of getting a tuition fee waiver with this. Other colleges will be GEC Ujjain (government). Or Private be (LNCT Bhopal, Acropolis and Medicaps Indore).
Best of luck.

If you belong to General, along with home state quota, you need around 145 marks in JEE Mains or a rank around 35 thousand to be able to get a seat in it. Moreover, a better rank than these will reward you better branch respectively.
Best of luck.

Kindly refer to my answer below to get this year CSE scenario in GSITS:
https://ask.shiksha.com/what-is-the-cut-off-for-cs-branch-in-sgsits-Indore-qna-3517379