The easiest way and most preferred is to book taxi car for the entire trip. This hired car can help you transfer from Delhi airport to the hotel and for conducting Intra travel and sightseeing. Another option is that you can just book Ola or Uber car for the pick up from the airport and thereafter transfer. For the tour you can pre-book national permit taxi cab which can pick you from the hotel and conduct sightseeing for couple of days. There are well known transport services and car rental agencies in Delhi such as Mann Tours, Doaba Transport Services, KTC, SAM Tours & Travels etc. You can get a quote from either of those or get from other sources.
In case you want to enjoy a train journey in Golden Triangle tour you can prefer travelling from Delhi to Agra by Gatimaan Express. This journey would take nearly one and half hour. This avails you the opportunity to visit the major highlights of Agra-Taj Mahal & Agra Fort in one day. After coming to Agra visiting these places you can move to Jaipur the same day by evening train by road. Khajuraho Udaipur intercity is a good option. If you travel by car to Jaipur it will take the sometime as by train. You can possibility reach by late night in Jaipur.
Delhi to Jaipur journey can be love easily by air, train or road trip. If you want to do Delhi to Jaipur trip in 1 day you have the best option to hire a car from Delhi, if you plan for Jaipur overnight tour from Delhi you can either use flight or train. If you travel by train or by air to Jaipur you need to pre book your taxi car for transfer and sightseeing.
Jaipur to Agra tour can be easily done by train or by car you can book car from Jaipur hold or from any car rental company in Jaipur. You can plan for one overnight Agra tour from Jaipur.