Yeah i think one of the worst things I remember when it comes to animal cruelty was walking around the Chatuchak Market in Bangkok. The animals were being so badly mistreated... put in extremely small cages with no water, no food, no love, no nothing! I couldn't stand it and had to leave!
Delhi-Agra-Jaipur is a good option while you are in Delhi. My advice would be to take a flight to Trivandrum. Airdeccan goes from del -to TRV , takes 4 1/2 hours only fare roughly aroung Rs. 2000/- which is $45 only. There is lot to be seen in south India. Kerala is another beautiful state in south where you can get to stay near the backwaters. You can visit the state of Rajsthan once you reach jaipur, its one of the most colorful states of India. Live with the people here, as the culture needs to be experienced closely. People are normally very friendle, but be cautious near the airports.
For taking a flight from Denmark to Delhi , you could try logging into www.airlines17.com. it gives various options that you could use. For staying in Jaipur, I would like to recommend 'Arya Nivas' which provides very good homely food and environment at very reasonable rates. Its really worth it.
Well, You have made up your mind to travel by Train. so will not say about a plane travel.
People have said, India is slow & slow trains. I dont agree
Catch Up Superfast trains like (Rajdhani, Shatabdi, Karnataka Express)
From Delhi to Bangalore. You can reach real fast.
From Bangalore, you can catch up a bus/train & reach there fast.
Have a nice journey.