I have traveled in 37 different countries so far, but most of the time it was for business and not too much family with me. It can be very enlightening and my only regret was not to add a day or so to really appreciate the country.
The first thing is to use common sense to initially avoid the things that seem obvious. Some countries turn out to be very safe because of the customs or laws, even though they look bad. A little local checking will quickly sort out the good from the bad.
India can look questionable, but the people are very passive and honest and theft is rare. Beggars are a nuisance, but leave once you say no or show you are not interested.
On my first trip to China, I was worried while in a taxi to my hotel through unlit streets (common in many areas a while ago). After checking, in I walked down a lit street to have a pizza and discovered my billfold was missing and went to the hotel service desk to report it and described it and the contents ($87.00) since I always separate my cash. The next morning, I got my billfold back complete with $87.00 in American money, but it included two American $1 bills but I neglected to say part of my cash was Canadian and not American. - The Chinese government is very strict and will not allow an foreigner to have a problem while in the country. If they caught the person with my billfold, he might be dead by now.
It really did bother me to leave my passport at the desk (common in many countries) when I checked in and then leave the room key at the desk when I left to get back my passport, but I found there are reasons. In India, I asked why and the desk manage said they make a copy of the passport if you lose it and they give you a certified copy until you get a replacement. Since India (in International hotels and better Indian hotels (Taj, Oberoi and even Holiday Inn, Days Inn, etc.) have so much electronic technology the records use is astonishing. Usually, I stopped at good hotel when arriving late (U.S. time) and used the "free" hotel ride to talk to the driver about the area. What gets scary is when you check into chain hotel at 11:00 PM for the first time and they ask you if you wanted the same meal order you had at another hotel a couple of months earlier. The visual recognition cameras also were a puzzel since when I came in, I was identified and the desk clerk already had my room key available and called me by name. This was in better hotels that can be very costly, but if a local person or company makes the reservation the cosy is about 50% of what the normal rates are.