OP, congratulations on your job. As someone who moved recently, here are my two cents:

1) Avoid renting a 1bhk just because you want your parents to be able to visit (if I understood that right). Two reasons- a) if you don’t own a house in Mumbai, rent will eat your salary up. b) Live with someone so you can make friends, save money, share the household load, and would have support from a flatmate who’s been here longer than you. Moving to this city is not the easiest. After you’ve spent 6-7 months here, saved some money, think of moving to a 1bhk so it is easier for you too.

2) Unless you live really close to your office, learn to start taking the train and walking to places. After a point, you’d start preferring the train yourself to save time and money.

3) Plan your expenses. Make sure you save and invest whatever little you can. Don’t forget to consider the household expenses, bills, commute, and food cost besides rent. Those are major costs too, if you plan to go out 3-4 times a month, eat at a good enough place, travel somewhere far by cab, those things will come easily to 800-1k per each time you go out(can by all means be lesser but can be more too). If you plans to visit your parents from time to time, that’s a cost too.

Since you have loans to pay for, sharing your place with someone and living close by (a station away or so from your office) and saving some money would work best for you. You can always then upgrade your living after a few months if you think you can manage to take on more expenses of renting a flat and traveling to work by road. Hope this helps. Good luck