Hee hee,that itinery sounds better :) You can travel by intercity and local buses on this route and on some can use overnight buses to save on bed fee's.Ist>>Selçuk,Pamukkale>>Göreme and Ankara>>Istanbul can all be by overnight bus so that's 3 nights you won't have to pay for hostels.
In each of the places you'll visit there are a good number of hostels to choose from.These days most hostels provide both dorm and private room options and todays hostels are usually very modern and clean with lot's of great facilities.The days of dirty flea pit flop houses has long gone!
To give you an idea of daily expenses,especially entrance fee's....
Istanbul.
Hagia Sofia-30TL
Topkapı Palace -30TL(Harem section extra 15TL)
Galata Tower- 20TL
Basilica Cisterns -10TL.
Archeological Museum -15TL
All mosques are free to enter.
Selçuk.
Ephesus -30TL(Terrace Houses an extra 15TL)
Mary's House- 10TL
Museum -10TL
Pamukkale.
Hierapolis and travertines -20TL
Cappadocia.
Göreme Open Air Museum -15TL plus a cover charge for some of the churches.
Zelve Open Air Museum -8TL
Ankara.
Museum of Anatolian Civilisations-15TL
This just gives you an idea of the major must see's but there may be others you want to visit.On a tight budget you may need to just pick out a couple and skip others.
If you can manage to increase your budget a bit it would be better for you but now you need to sit down and work out how much you will need in total for transport,accomodation,entrance fee's and then allow a few dollars a day for simple food eating in the small lokanta's used by local people(these are clean,cheap and serve great food!)and see how much it works out at per day per person.
BTW,most hostels also include breakfast in the price so you can fill up on these in the morning.
You probably can do it on 35-45$ but...it is always useful to have a bit extra just in case of emergencies or unexpected expenses :)