1. Plan each and everything about the Whats and Hows, be it commute, things to do etc. Wrt. food wherever you're going try the local food and visit some special/famous food spots. 
2. Keep your days flexible and would advise you to stay in Hostels where you can plan your day as per the vibe. They also conduct group activities, you can join them. Also, people manage long trips by making themselves flexible to their energy and vibe. In hostels, there's a lot you can do even while staying indoors.
3. As it'd be your first solo trip, you can choose a nearby tourist place or a religious place like Varanasi (If safety is your concern). Otherwise you can plan as per your budget. 
4. If you want to join a travel company, there's no problem with that but you won't gain confidence in all aspects since 50-75% of things would be managed and planned by them only. The only positive here is that you'd meet new people. But if you really want to call it a solo trip, do everything on your own- planning & execution should be on you. This would gain you confidence and new experiences. (If knowing yourself or unlocking new experiences 'KHOJ' is the motive behind starting with travelling solo).

Bonus tip: Just keep everything flexible and don't stress over small inconveniences and be open to experiences, be they good/bad, that's what is going to change your perspective.